{"id":"https://openalex.org/W1999770809","doi":"https://doi.org/10.1142/s0218196714500271","title":"Shifts of generators and delta sets of numerical monoids","display_name":"Shifts of generators and delta sets of numerical monoids","publication_year":2014,"publication_date":"2014-07-02","ids":{"openalex":"https://openalex.org/W1999770809","doi":"https://doi.org/10.1142/s0218196714500271","mag":"1999770809"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196714500271","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196714500271","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":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006699882","display_name":"Scott T. Chapman","orcid":"https://orcid.org/0000-0003-1205-6899"},"institutions":[{"id":"https://openalex.org/I191429286","display_name":"Sam Houston State University","ror":"https://ror.org/00yh3cz06","country_code":"US","type":"education","lineage":["https://openalex.org/I191429286"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"S. T. Chapman","raw_affiliation_strings":["Department of Mathematics and Statistics, Sam Houston State University, Box 2206, Huntsville, TX 77341-2206, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Sam Houston State University, Box 2206, Huntsville, TX 77341-2206, USA","institution_ids":["https://openalex.org/I191429286"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084890905","display_name":"Nathan O. Kaplan","orcid":"https://orcid.org/0000-0001-5305-983X"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nathan Kaplan","raw_affiliation_strings":["Department of Mathematics, Princeton University, Princeton NJ 08544-1000, USA","Department of Mathematics, Princeton University. Princeton, NJ 08544-1000, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Princeton University, Princeton NJ 08544-1000, USA","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Department of Mathematics, Princeton University. Princeton, NJ 08544-1000, USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070552352","display_name":"Tyler Lemburg","orcid":null},"institutions":[{"id":"https://openalex.org/I114395901","display_name":"University of Nebraska\u2013Lincoln","ror":"https://ror.org/043mer456","country_code":"US","type":"education","lineage":["https://openalex.org/I114395901"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tyler Lemburg","raw_affiliation_strings":["Department of Mathematics, University of Nebraska at Lincoln, 203 Avery Hall, Lincoln, NE 68588-0130, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Nebraska at Lincoln, 203 Avery Hall, Lincoln, NE 68588-0130, USA","institution_ids":["https://openalex.org/I114395901"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052748777","display_name":"Andrew Niles","orcid":null},"institutions":[{"id":"https://openalex.org/I5388228","display_name":"University of Rochester","ror":"https://ror.org/022kthw22","country_code":"US","type":"education","lineage":["https://openalex.org/I5388228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew Niles","raw_affiliation_strings":["Department of Mathematics, University of Rochester, Hylan Building, Rochester, NY 14627, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Rochester, Hylan Building, Rochester, NY 14627, USA","institution_ids":["https://openalex.org/I5388228"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006296667","display_name":"Christina Zlogar","orcid":null},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christina Zlogar","raw_affiliation_strings":["Department of Mathematics, Cornell University, 310 Malott Hall, Ithaca, NY 14853-4201, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Cornell University, 310 Malott Hall, Ithaca, NY 14853-4201, USA","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5006699882"],"corresponding_institution_ids":["https://openalex.org/I191429286"],"apc_list":null,"apc_paid":null,"fwci":3.4805,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.91730505,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"24","issue":"05","first_page":"655","last_page":"669"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9997000098228455,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9997000098228455,"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/T12069","display_name":"Commutative Algebra and Its Applications","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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9818999767303467,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8169959783554077},{"id":"https://openalex.org/keywords/monoid","display_name":"Monoid","score":0.763725996017456},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7409332990646362},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.6927794218063354},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6812160611152649},{"id":"https://openalex.org/keywords/numerical-semigroup","display_name":"Numerical semigroup","score":0.5034200549125671},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.4910738468170166},{"id":"https://openalex.org/keywords/prime-factor","display_name":"Prime factor","score":0.42252978682518005},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3473619818687439},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08965006470680237},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.07399553060531616}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8169959783554077},{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.763725996017456},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7409332990646362},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.6927794218063354},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6812160611152649},{"id":"https://openalex.org/C2779628518","wikidata":"https://www.wikidata.org/wiki/Q7069664","display_name":"Numerical semigroup","level":3,"score":0.5034200549125671},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4910738468170166},{"id":"https://openalex.org/C30860621","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime factor","level":3,"score":0.42252978682518005},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3473619818687439},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08965006470680237},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.07399553060531616},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0218196714500271","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196714500271","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:CiteSeerX.psu:10.1.1.210.684","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.210.684","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.shsu.edu/~stc008/finalshiftsofgenerators.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.78.2625","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.78.2625","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.trinity.edu/schapman/finalshiftsofgenerators.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W651067426","https://openalex.org/W1138798142","https://openalex.org/W1415576118","https://openalex.org/W1968757433","https://openalex.org/W1974879893","https://openalex.org/W2009744824","https://openalex.org/W2054881696","https://openalex.org/W2124552613","https://openalex.org/W2332901121","https://openalex.org/W2736107074","https://openalex.org/W2799237516"],"related_works":["https://openalex.org/W4205186527","https://openalex.org/W2348092648","https://openalex.org/W2054570290","https://openalex.org/W4381573103","https://openalex.org/W4295997284","https://openalex.org/W1528360103","https://openalex.org/W2022996787","https://openalex.org/W2375604274","https://openalex.org/W2963287447","https://openalex.org/W4213038763"],"abstract_inverted_index":{"Let":[0,141],"S":[1,96],"be":[2,151],"a":[3,31,179,193,225],"numerical":[4,129,180],"monoid":[5,181],"with":[6],"minimal":[7],"generating":[8],"set":[9,62,72,94],"\u3008n":[10],"1":[11,42,56,86,143,166,215],",":[12,43,144,147,167,172],"\u2026,":[13,44,148,173],"n":[14,160,163,168,174,183,200,205],"t":[15,150,177,210],"\u3009.":[16],"For":[17],"m":[18,45,49,52,74,83],"\u2208":[19],"S,":[20],"if":[21,199],"[Formula:":[22,26],"see":[23,27],"text],":[24],"then":[25,203,222],"text]":[28],"is":[29,75,184,230],"called":[30],"factorization":[32,66],"length":[33],"of":[34,63,68,73,95,111,128,155],"m.":[35,69],"We":[36,188],"denote":[37],"by":[38,77,97],"\u2112(m)":[39],"=":[40,79,99,161,207,211],"{m":[41,80],"k":[46],"}":[47],"(where":[48],"i":[50,58,84,88],"<":[51,59,89],"i+1":[53,81],"for":[54,227],"each":[55],"\u2264":[57,87],"k)":[60],"the":[61,92,109,138],"all":[64],"possible":[65],"lengths":[67],"The":[70],"Delta":[71,93],"defined":[76],"\u0394(m)":[78],"-":[82],"|":[85],"k}":[90],"and":[91,122,158,213,216],"\u0394(S)":[98,112],"\u22c3":[100],"m\u2208S":[101],"\u0394(m).":[102],"In":[103],"this":[104],"paper,":[105],"we":[106,223],"expand":[107],"on":[108],"study":[110],"begun":[113],"in":[114,137],"[C.":[115],"Bowles,":[116],"S.":[117],"T.":[118],"Chapman,":[119],"N.":[120],"Kaplan":[121],"D.":[123],"Reiser,":[124],"On":[125],"delta":[126],"sets":[127],"monoids,":[130],"J.":[131],"Algebra":[132],"Appl.":[133],"5":[134],"(2006)":[135],"1\u201324]":[136],"following":[139],"manner.":[140],"r":[142,145,149,165,170,176,214,217],"2":[146,171,212,218],"an":[152],"increasing":[153],"sequence":[154],"positive":[156,186,194],"integers":[157],"M":[159],"\u3008n,":[162],"+":[164,169,175],"\u3009":[178],"where":[182],"some":[185],"integer.":[187],"prove":[189],"that":[190,198],"there":[191],"exists":[192],"integer":[195],"N":[196,202,228],"such":[197],">":[201],"|\u0394(M":[204],")|":[206],"1.":[208],"If":[209],"are":[219],"relatively":[220],"prime,":[221],"determine":[224],"value":[226],"which":[229],"sharp.":[231]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}