{"id":"https://openalex.org/W2584834045","doi":"https://doi.org/10.1142/s0218196718500030","title":"Minimal presentations of shifted numerical monoids","display_name":"Minimal presentations of shifted numerical monoids","publication_year":2017,"publication_date":"2017-11-14","ids":{"openalex":"https://openalex.org/W2584834045","doi":"https://doi.org/10.1142/s0218196718500030","mag":"2584834045"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196718500030","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196718500030","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1701.08555","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038971459","display_name":"Rebecca Conaway","orcid":null},"institutions":[{"id":"https://openalex.org/I174154184","display_name":"Lee University","ror":"https://ror.org/00fwhaq79","country_code":"US","type":"education","lineage":["https://openalex.org/I174154184"]},{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]},{"id":"https://openalex.org/I141450709","display_name":"Monmouth University","ror":"https://ror.org/01d6qxv05","country_code":"US","type":"education","lineage":["https://openalex.org/I141450709"]},{"id":"https://openalex.org/I78715868","display_name":"University of Arkansas at Fayetteville","ror":"https://ror.org/05jbt9m15","country_code":"US","type":"education","lineage":["https://openalex.org/I78715868"]},{"id":"https://openalex.org/I35722693","display_name":"University of Hawaii at Hilo","ror":"https://ror.org/02mp2av58","country_code":"US","type":"education","lineage":["https://openalex.org/I35722693"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Rebecca Conaway","raw_affiliation_strings":["Monmouth University, West Long Branch, NJ 07764, USA","Mathematics Department, UC Berkeley, Berkeley, CA 94720","Mathematics Department, University of Hawai'i at Hilo, Hilo, HI 96720","Lee University, Cleveland, TN 37311","Mathematics Department, Texas A&M University, College Station, TX 77843","University of Arkansas, Fayetteville, AR 72701"],"affiliations":[{"raw_affiliation_string":"Monmouth University, West Long Branch, NJ 07764, USA","institution_ids":["https://openalex.org/I141450709"]},{"raw_affiliation_string":"Mathematics Department, UC Berkeley, Berkeley, CA 94720","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Mathematics Department, University of Hawai'i at Hilo, Hilo, HI 96720","institution_ids":["https://openalex.org/I35722693"]},{"raw_affiliation_string":"Lee University, Cleveland, TN 37311","institution_ids":["https://openalex.org/I174154184"]},{"raw_affiliation_string":"Mathematics Department, Texas A&M University, College Station, TX 77843","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"University of Arkansas, Fayetteville, AR 72701","institution_ids":["https://openalex.org/I78715868"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066438959","display_name":"Felix Gotti","orcid":"https://orcid.org/0000-0002-5313-2141"},"institutions":[{"id":"https://openalex.org/I35722693","display_name":"University of Hawaii at Hilo","ror":"https://ror.org/02mp2av58","country_code":"US","type":"education","lineage":["https://openalex.org/I35722693"]},{"id":"https://openalex.org/I141450709","display_name":"Monmouth University","ror":"https://ror.org/01d6qxv05","country_code":"US","type":"education","lineage":["https://openalex.org/I141450709"]},{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]},{"id":"https://openalex.org/I78715868","display_name":"University of Arkansas at Fayetteville","ror":"https://ror.org/05jbt9m15","country_code":"US","type":"education","lineage":["https://openalex.org/I78715868"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]},{"id":"https://openalex.org/I174154184","display_name":"Lee University","ror":"https://ror.org/00fwhaq79","country_code":"US","type":"education","lineage":["https://openalex.org/I174154184"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Felix Gotti","raw_affiliation_strings":["Mathematics Department, UC Berkeley, Berkeley, CA 94720, USA","Mathematics Department, Texas A&M University, College Station, TX 77843","Monmouth University, West Long Branch, NJ 07764","University of Arkansas, Fayetteville, AR 72701","Mathematics Department, University of Hawai'i at Hilo, Hilo, HI 96720","Lee University, Cleveland, TN 37311"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, UC Berkeley, Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Mathematics Department, Texas A&M University, College Station, TX 77843","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Monmouth University, West Long Branch, NJ 07764","institution_ids":["https://openalex.org/I141450709"]},{"raw_affiliation_string":"University of Arkansas, Fayetteville, AR 72701","institution_ids":["https://openalex.org/I78715868"]},{"raw_affiliation_string":"Mathematics Department, University of Hawai'i at Hilo, Hilo, HI 96720","institution_ids":["https://openalex.org/I35722693"]},{"raw_affiliation_string":"Lee University, Cleveland, TN 37311","institution_ids":["https://openalex.org/I174154184"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067201963","display_name":"Jesse Horton","orcid":null},"institutions":[{"id":"https://openalex.org/I78715868","display_name":"University of Arkansas at Fayetteville","ror":"https://ror.org/05jbt9m15","country_code":"US","type":"education","lineage":["https://openalex.org/I78715868"]},{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]},{"id":"https://openalex.org/I141450709","display_name":"Monmouth University","ror":"https://ror.org/01d6qxv05","country_code":"US","type":"education","lineage":["https://openalex.org/I141450709"]},{"id":"https://openalex.org/I174154184","display_name":"Lee University","ror":"https://ror.org/00fwhaq79","country_code":"US","type":"education","lineage":["https://openalex.org/I174154184"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]},{"id":"https://openalex.org/I35722693","display_name":"University of Hawaii at Hilo","ror":"https://ror.org/02mp2av58","country_code":"US","type":"education","lineage":["https://openalex.org/I35722693"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jesse Horton","raw_affiliation_strings":["University of Arkansas, Fayetteville, AR 72701, USA","Monmouth University, West Long Branch, NJ 07764","Mathematics Department, University of Hawai'i at Hilo, Hilo, HI 96720","Lee University, Cleveland, TN 37311","Mathematics Department, Texas A&M University, College Station, TX 77843","Mathematics Department, UC Berkeley, Berkeley, CA 94720"],"affiliations":[{"raw_affiliation_string":"University of Arkansas, Fayetteville, AR 72701, USA","institution_ids":["https://openalex.org/I78715868"]},{"raw_affiliation_string":"Monmouth University, West Long Branch, NJ 07764","institution_ids":["https://openalex.org/I141450709"]},{"raw_affiliation_string":"Mathematics Department, University of Hawai'i at Hilo, Hilo, HI 96720","institution_ids":["https://openalex.org/I35722693"]},{"raw_affiliation_string":"Lee University, Cleveland, TN 37311","institution_ids":["https://openalex.org/I174154184"]},{"raw_affiliation_string":"Mathematics Department, Texas A&M University, College Station, TX 77843","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Mathematics Department, UC Berkeley, Berkeley, CA 94720","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003995796","display_name":"Christopher O\u2019Neill","orcid":null},"institutions":[{"id":"https://openalex.org/I78715868","display_name":"University of Arkansas at Fayetteville","ror":"https://ror.org/05jbt9m15","country_code":"US","type":"education","lineage":["https://openalex.org/I78715868"]},{"id":"https://openalex.org/I174154184","display_name":"Lee University","ror":"https://ror.org/00fwhaq79","country_code":"US","type":"education","lineage":["https://openalex.org/I174154184"]},{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]},{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]},{"id":"https://openalex.org/I141450709","display_name":"Monmouth University","ror":"https://ror.org/01d6qxv05","country_code":"US","type":"education","lineage":["https://openalex.org/I141450709"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christopher O\u2019Neill","raw_affiliation_strings":["Mathematics Department, University of California Davis, Davis, CA 95616, USA","Lee University, Cleveland, TN 37311","Mathematics Department, Texas A&M University, College Station, TX 77843","Mathematics Department, UC Berkeley, Berkeley, CA 94720","University of Arkansas, Fayetteville, AR 72701","Monmouth University, West Long Branch, NJ 07764"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, University of California Davis, Davis, CA 95616, USA","institution_ids":["https://openalex.org/I84218800"]},{"raw_affiliation_string":"Lee University, Cleveland, TN 37311","institution_ids":["https://openalex.org/I174154184"]},{"raw_affiliation_string":"Mathematics Department, Texas A&M University, College Station, TX 77843","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Mathematics Department, UC Berkeley, Berkeley, CA 94720","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"University of Arkansas, Fayetteville, AR 72701","institution_ids":["https://openalex.org/I78715868"]},{"raw_affiliation_string":"Monmouth University, West Long Branch, NJ 07764","institution_ids":["https://openalex.org/I141450709"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071992162","display_name":"Roberto Pelayo","orcid":null},"institutions":[{"id":"https://openalex.org/I141450709","display_name":"Monmouth University","ror":"https://ror.org/01d6qxv05","country_code":"US","type":"education","lineage":["https://openalex.org/I141450709"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]},{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]},{"id":"https://openalex.org/I78715868","display_name":"University of Arkansas at Fayetteville","ror":"https://ror.org/05jbt9m15","country_code":"US","type":"education","lineage":["https://openalex.org/I78715868"]},{"id":"https://openalex.org/I174154184","display_name":"Lee University","ror":"https://ror.org/00fwhaq79","country_code":"US","type":"education","lineage":["https://openalex.org/I174154184"]},{"id":"https://openalex.org/I35722693","display_name":"University of Hawaii at Hilo","ror":"https://ror.org/02mp2av58","country_code":"US","type":"education","lineage":["https://openalex.org/I35722693"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Roberto Pelayo","raw_affiliation_strings":["Mathematics Department, University of Hawai\u2018i at Hilo, Hilo, HI 96720, USA","Mathematics Department, Texas A&M University, College Station, TX 77843","Monmouth University, West Long Branch, NJ 07764","Lee University, Cleveland, TN 37311","Mathematics Department, UC Berkeley, Berkeley, CA 94720","University of Arkansas, Fayetteville, AR 72701"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, University of Hawai\u2018i at Hilo, Hilo, HI 96720, USA","institution_ids":["https://openalex.org/I35722693"]},{"raw_affiliation_string":"Mathematics Department, Texas A&M University, College Station, TX 77843","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Monmouth University, West Long Branch, NJ 07764","institution_ids":["https://openalex.org/I141450709"]},{"raw_affiliation_string":"Lee University, Cleveland, TN 37311","institution_ids":["https://openalex.org/I174154184"]},{"raw_affiliation_string":"Mathematics Department, UC Berkeley, Berkeley, CA 94720","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"University of Arkansas, Fayetteville, AR 72701","institution_ids":["https://openalex.org/I78715868"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033233505","display_name":"Mesa Pracht","orcid":null},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]},{"id":"https://openalex.org/I174154184","display_name":"Lee University","ror":"https://ror.org/00fwhaq79","country_code":"US","type":"education","lineage":["https://openalex.org/I174154184"]},{"id":"https://openalex.org/I78715868","display_name":"University of Arkansas at Fayetteville","ror":"https://ror.org/05jbt9m15","country_code":"US","type":"education","lineage":["https://openalex.org/I78715868"]},{"id":"https://openalex.org/I141450709","display_name":"Monmouth University","ror":"https://ror.org/01d6qxv05","country_code":"US","type":"education","lineage":["https://openalex.org/I141450709"]},{"id":"https://openalex.org/I35722693","display_name":"University of Hawaii at Hilo","ror":"https://ror.org/02mp2av58","country_code":"US","type":"education","lineage":["https://openalex.org/I35722693"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mesa Pracht","raw_affiliation_strings":["Lee University, Cleveland, TN 37311, USA","Mathematics Department, UC Berkeley, Berkeley, CA 94720","Mathematics Department, University of Hawai'i at Hilo, Hilo, HI 96720","Mathematics Department, Texas A&M University, College Station, TX 77843","Monmouth University, West Long Branch, NJ 07764","University of Arkansas, Fayetteville, AR 72701"],"affiliations":[{"raw_affiliation_string":"Lee University, Cleveland, TN 37311, USA","institution_ids":["https://openalex.org/I174154184"]},{"raw_affiliation_string":"Mathematics Department, UC Berkeley, Berkeley, CA 94720","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Mathematics Department, University of Hawai'i at Hilo, Hilo, HI 96720","institution_ids":["https://openalex.org/I35722693"]},{"raw_affiliation_string":"Mathematics Department, Texas A&M University, College Station, TX 77843","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Monmouth University, West Long Branch, NJ 07764","institution_ids":["https://openalex.org/I141450709"]},{"raw_affiliation_string":"University of Arkansas, Fayetteville, AR 72701","institution_ids":["https://openalex.org/I78715868"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032428259","display_name":"Brian Wissman","orcid":null},"institutions":[{"id":"https://openalex.org/I174154184","display_name":"Lee University","ror":"https://ror.org/00fwhaq79","country_code":"US","type":"education","lineage":["https://openalex.org/I174154184"]},{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]},{"id":"https://openalex.org/I141450709","display_name":"Monmouth University","ror":"https://ror.org/01d6qxv05","country_code":"US","type":"education","lineage":["https://openalex.org/I141450709"]},{"id":"https://openalex.org/I78715868","display_name":"University of Arkansas at Fayetteville","ror":"https://ror.org/05jbt9m15","country_code":"US","type":"education","lineage":["https://openalex.org/I78715868"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]},{"id":"https://openalex.org/I35722693","display_name":"University of Hawaii at Hilo","ror":"https://ror.org/02mp2av58","country_code":"US","type":"education","lineage":["https://openalex.org/I35722693"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Brian Wissman","raw_affiliation_strings":["Mathematics Department, University of Hawai\u2018i at Hilo, Hilo, HI 96720, USA","Lee University, Cleveland, TN 37311","University of Arkansas, Fayetteville, AR 72701","Monmouth University, West Long Branch, NJ 07764","Mathematics Department, UC Berkeley, Berkeley, CA 94720","Mathematics Department, Texas A&M University, College Station, TX 77843"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, University of Hawai\u2018i at Hilo, Hilo, HI 96720, USA","institution_ids":["https://openalex.org/I35722693"]},{"raw_affiliation_string":"Lee University, Cleveland, TN 37311","institution_ids":["https://openalex.org/I174154184"]},{"raw_affiliation_string":"University of Arkansas, Fayetteville, AR 72701","institution_ids":["https://openalex.org/I78715868"]},{"raw_affiliation_string":"Monmouth University, West Long Branch, NJ 07764","institution_ids":["https://openalex.org/I141450709"]},{"raw_affiliation_string":"Mathematics Department, UC Berkeley, Berkeley, CA 94720","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Mathematics Department, Texas A&M University, College Station, TX 77843","institution_ids":["https://openalex.org/I91045830"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5038971459"],"corresponding_institution_ids":["https://openalex.org/I141450709","https://openalex.org/I174154184","https://openalex.org/I35722693","https://openalex.org/I78715868","https://openalex.org/I91045830","https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":1.7586,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.81109107,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"28","issue":"01","first_page":"53","last_page":"68"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/monoid","display_name":"Monoid","score":0.9177443981170654},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8832669258117676},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.6900399923324585},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.6158263683319092},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6125615835189819},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.5085984468460083},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4275187849998474},{"id":"https://openalex.org/keywords/syntactic-monoid","display_name":"Syntactic monoid","score":0.41161012649536133},{"id":"https://openalex.org/keywords/free-monoid","display_name":"Free monoid","score":0.405517041683197},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3588781952857971},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35294824838638306},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3285967707633972},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10360673069953918},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.08982455730438232}],"concepts":[{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.9177443981170654},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8832669258117676},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.6900399923324585},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.6158263683319092},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6125615835189819},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5085984468460083},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4275187849998474},{"id":"https://openalex.org/C119903167","wikidata":"https://www.wikidata.org/wiki/Q3321297","display_name":"Syntactic monoid","level":4,"score":0.41161012649536133},{"id":"https://openalex.org/C149685015","wikidata":"https://www.wikidata.org/wiki/Q5500266","display_name":"Free monoid","level":3,"score":0.405517041683197},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3588781952857971},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35294824838638306},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3285967707633972},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10360673069953918},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.08982455730438232},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218196718500030","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196718500030","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1701.08555","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1701.08555","pdf_url":"https://arxiv.org/pdf/1701.08555","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1701.08555","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1701.08555","pdf_url":"https://arxiv.org/pdf/1701.08555","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W651067426","https://openalex.org/W1501065599","https://openalex.org/W1518341038","https://openalex.org/W1550656971","https://openalex.org/W1971711113","https://openalex.org/W1973128036","https://openalex.org/W1999770809","https://openalex.org/W2003298801","https://openalex.org/W2009744824","https://openalex.org/W2111674339","https://openalex.org/W2134709631","https://openalex.org/W2189625324","https://openalex.org/W2278857362","https://openalex.org/W2963143821","https://openalex.org/W3100436337","https://openalex.org/W3103836590","https://openalex.org/W4237442181","https://openalex.org/W4240837394"],"related_works":["https://openalex.org/W51936586","https://openalex.org/W3161268522","https://openalex.org/W3143205136","https://openalex.org/W2071633178","https://openalex.org/W2971508078","https://openalex.org/W2038387119","https://openalex.org/W3201418638","https://openalex.org/W2090238248","https://openalex.org/W3133734481","https://openalex.org/W2079194245"],"abstract_inverted_index":{"A":[0],"numerical":[1,13],"monoid":[2,14],"is":[3,58,66],"an":[4],"additive":[5],"submonoid":[6],"of":[7,21,36,50,89],"the":[8,19,48,69],"non-negative":[9],"integers.":[10],"Given":[11],"a":[12,63,86],"[Formula:":[15,24,30,37,51,55,72],"see":[16,25,31,38,52,56,73],"text],":[17],"consider":[18],"family":[20],"\u201cshifted\u201d":[22],"monoids":[23],"text]":[26,32,53,57],"obtained":[27],"by":[28],"adding":[29],"to":[33,79],"each":[34],"generator":[35],"text].":[39,74],"In":[40],"this":[41],"paper,":[42],"we":[43],"examine":[44],"minimal":[45],"relations":[46],"among":[47],"generators":[49],"when":[54],"sufficiently":[59],"large,":[60],"culminating":[61],"in":[62,68],"description":[64],"that":[65],"periodic":[67],"shift":[70],"parameter":[71],"We":[75],"explore":[76],"several":[77],"applications":[78],"computation":[80],"and":[81,84],"factorization":[82],"theory,":[83],"improve":[85],"recent":[87],"result":[88],"Thanh":[90],"Vu":[91],"from":[92],"combinatorial":[93],"commutative":[94],"algebra.":[95]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}