{"id":"https://openalex.org/W3056982588","doi":"https://doi.org/10.1142/s0218196721500417","title":"Numerical semigroups of small and large type","display_name":"Numerical semigroups of small and large type","publication_year":2021,"publication_date":"2021-05-18","ids":{"openalex":"https://openalex.org/W3056982588","doi":"https://doi.org/10.1142/s0218196721500417","mag":"3056982588"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196721500417","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196721500417","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2008.08110","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065125948","display_name":"Deepesh Singhal","orcid":"https://orcid.org/0000-0003-1317-5523"},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Deepesh Singhal","raw_affiliation_strings":["University of California, Irvine, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Irvine, USA","institution_ids":["https://openalex.org/I204250578"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5065125948"],"corresponding_institution_ids":["https://openalex.org/I204250578"],"apc_list":null,"apc_paid":null,"fwci":0.629,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.56982569,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"31","issue":"05","first_page":"883","last_page":"902"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9843999743461609,"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"}},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.968500018119812,"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/numerical-semigroup","display_name":"Numerical semigroup","score":0.9167202711105347},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7745823860168457},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.7006103992462158},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.6959641575813293},{"id":"https://openalex.org/keywords/genus","display_name":"Genus","score":0.5885977149009705},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.5175235271453857},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5007622241973877},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4690948724746704},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4337823688983917},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39251577854156494},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.376390278339386},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25110214948654175},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.04272237420082092}],"concepts":[{"id":"https://openalex.org/C2779628518","wikidata":"https://www.wikidata.org/wiki/Q7069664","display_name":"Numerical semigroup","level":3,"score":0.9167202711105347},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7745823860168457},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.7006103992462158},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6959641575813293},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.5885977149009705},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.5175235271453857},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5007622241973877},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4690948724746704},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4337823688983917},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39251577854156494},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.376390278339386},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25110214948654175},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.04272237420082092},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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":4,"locations":[{"id":"doi:10.1142/s0218196721500417","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196721500417","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:2008.08110","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2008.08110","pdf_url":"https://arxiv.org/pdf/2008.08110","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"},{"id":"mag:3056982588","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2008.08110.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2008.08110","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2008.08110","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2008.08110","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2008.08110","pdf_url":"https://arxiv.org/pdf/2008.08110","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1980041466","https://openalex.org/W1994828121","https://openalex.org/W1995384533","https://openalex.org/W1998390807","https://openalex.org/W2020485388","https://openalex.org/W2038866204","https://openalex.org/W2079513712","https://openalex.org/W2147044958","https://openalex.org/W2530426970","https://openalex.org/W2594384156","https://openalex.org/W2908245283","https://openalex.org/W2929318751","https://openalex.org/W2962767902","https://openalex.org/W2963360633","https://openalex.org/W2963449727","https://openalex.org/W2963832740"],"related_works":["https://openalex.org/W3047903977","https://openalex.org/W2929318751","https://openalex.org/W2061948639","https://openalex.org/W3157076192","https://openalex.org/W2963535044","https://openalex.org/W3101886772","https://openalex.org/W3159470726","https://openalex.org/W3016972553","https://openalex.org/W2054267877","https://openalex.org/W2321128589","https://openalex.org/W2963749736","https://openalex.org/W1967161149","https://openalex.org/W2263249703","https://openalex.org/W1967224062","https://openalex.org/W2517911622","https://openalex.org/W2991824606","https://openalex.org/W2370084419","https://openalex.org/W1981186129","https://openalex.org/W3018351705","https://openalex.org/W1536167238"],"abstract_inverted_index":{"A":[0],"numerical":[1,22,46,75,93,117],"semigroup":[2,23,47],"is":[3,41,106,129],"a":[4,12,21,63,85],"sub-semigroup":[5],"of":[6,16,20,74,92,116],"the":[7,17,90],"natural":[8],"numbers":[9],"that":[10,43,66,83],"has":[11],"finite":[13],"complement.":[14],"Some":[15],"key":[18],"properties":[19],"are":[24,57],"its":[25],"Frobenius":[26,96],"number":[27,91,97,115],"[Formula:":[28,32,37,48,54,78,87,98,103,111,121,126,135],"see":[29,33,38,49,55,79,88,99,104,112,122,127,136],"text],":[30],"genus":[31,120],"text]":[34,56,89,100,105,123,128],"and":[35,101,124],"type":[36,102,125],"text].":[39,50,80,113,137],"It":[40],"known":[42],"for":[44,84,109,133],"any":[45],"Numerical":[51],"semigroups":[52,76,94,118],"with":[53,77,95,119],"called":[58],"almost":[59],"symmetric,":[60],"we":[61],"introduce":[62],"new":[64],"property":[65],"characterizes":[67],"them.":[68],"We":[69,81],"give":[70],"an":[71],"explicit":[72],"characterization":[73],"show":[82],"fixed":[86],"eventually":[107,131],"constant":[108,132],"large":[110,134],"The":[114],"also":[130]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}