{"id":"https://openalex.org/W2992658587","doi":"https://doi.org/10.5070/c61055385","title":"Numerical semigroups, polyhedra, and posets I: the group cone","display_name":"Numerical semigroups, polyhedra, and posets I: the group cone","publication_year":2021,"publication_date":"2021-12-09","ids":{"openalex":"https://openalex.org/W2992658587","doi":"https://doi.org/10.5070/c61055385","mag":"2992658587"},"language":"en","primary_location":{"id":"doi:10.5070/c61055385","is_oa":true,"landing_page_url":"https://doi.org/10.5070/c61055385","pdf_url":"https://escholarship.org/content/qt5b43h4dq/qt5b43h4dq.pdf?t=r96vm0","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://escholarship.org/content/qt5b43h4dq/qt5b43h4dq.pdf?t=r96vm0","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084890905","display_name":"Nathan O. Kaplan","orcid":"https://orcid.org/0000-0001-5305-983X"},"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":"Nathan Kaplan","raw_affiliation_strings":["University of California, Irvine, CA, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Irvine, CA, U.S.A","institution_ids":["https://openalex.org/I204250578"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003995796","display_name":"Christopher O\u2019Neill","orcid":null},"institutions":[{"id":"https://openalex.org/I26538001","display_name":"San Diego State University","ror":"https://ror.org/0264fdx42","country_code":"US","type":"education","lineage":["https://openalex.org/I26538001"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christopher O'Neill","raw_affiliation_strings":["San Diego State University, San Diego, CA, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"San Diego State University, San Diego, CA, U.S.A","institution_ids":["https://openalex.org/I26538001"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5084890905"],"corresponding_institution_ids":["https://openalex.org/I204250578"],"apc_list":null,"apc_paid":null,"fwci":2.5187,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.86026464,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"1","issue":"0","first_page":null,"last_page":null},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.9955999851226807,"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/polyhedron","display_name":"Polyhedron","score":0.9289689660072327},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.8998910784721375},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.6668949723243713},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6337854862213135},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.6088420748710632},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5940051078796387},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.5895808935165405},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5848240256309509},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.524445116519928},{"id":"https://openalex.org/keywords/finite-group","display_name":"Finite group","score":0.4272347688674927},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12728846073150635},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12357327342033386},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.0793013870716095},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.04999002814292908}],"concepts":[{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.9289689660072327},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.8998910784721375},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.6668949723243713},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6337854862213135},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.6088420748710632},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5940051078796387},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5895808935165405},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5848240256309509},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.524445116519928},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.4272347688674927},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12728846073150635},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12357327342033386},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0793013870716095},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.04999002814292908},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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":5,"locations":[{"id":"doi:10.5070/c61055385","is_oa":true,"landing_page_url":"https://doi.org/10.5070/c61055385","pdf_url":"https://escholarship.org/content/qt5b43h4dq/qt5b43h4dq.pdf?t=r96vm0","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1912.03741","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1912.03741","pdf_url":"https://arxiv.org/pdf/1912.03741","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:2992658587","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1912.03741.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":"pmh:oai:escholarship.org:ark:/13030/qt5b43h4dq","is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/5b43h4dq","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Combinatorial Theory, vol 1, iss 0","raw_type":"article"},{"id":"doi:10.48550/arxiv.1912.03741","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1912.03741","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-journal"}],"best_oa_location":{"id":"doi:10.5070/c61055385","is_oa":true,"landing_page_url":"https://doi.org/10.5070/c61055385","pdf_url":"https://escholarship.org/content/qt5b43h4dq/qt5b43h4dq.pdf?t=r96vm0","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2113302768","display_name":"Counting Problems in Number Theory: Elliptic and Plane Quartic Curves over Finite Fields","funder_award_id":"1802281","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2992658587.pdf","grobid_xml":"https://content.openalex.org/works/W2992658587.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W85113592","https://openalex.org/W350260367","https://openalex.org/W1931520163","https://openalex.org/W1982536303","https://openalex.org/W1999043701","https://openalex.org/W2041967853","https://openalex.org/W2065803772","https://openalex.org/W2079513712","https://openalex.org/W2108958829","https://openalex.org/W2243973406","https://openalex.org/W2319549236","https://openalex.org/W2482024337","https://openalex.org/W2492648862","https://openalex.org/W2914659449","https://openalex.org/W2946869046","https://openalex.org/W2963655230","https://openalex.org/W2994787567","https://openalex.org/W3085584770","https://openalex.org/W3099349302","https://openalex.org/W6603769561","https://openalex.org/W6629283939","https://openalex.org/W6638675383","https://openalex.org/W6815057685","https://openalex.org/W6824705359"],"related_works":["https://openalex.org/W2065803772","https://openalex.org/W3100332834","https://openalex.org/W2951010602","https://openalex.org/W2095207331","https://openalex.org/W2198935113","https://openalex.org/W2949692952","https://openalex.org/W2811483603","https://openalex.org/W2140504886","https://openalex.org/W1528227794","https://openalex.org/W3105922857","https://openalex.org/W2914923616","https://openalex.org/W3097037299","https://openalex.org/W2091667541","https://openalex.org/W1981342101","https://openalex.org/W2048564544","https://openalex.org/W2775518698","https://openalex.org/W2062938993","https://openalex.org/W2048781220","https://openalex.org/W2766788900","https://openalex.org/W3096016772"],"abstract_inverted_index":{"Several":[0],"recent":[1],"papers":[2],"have":[3],"explored":[4],"families":[5,17,71,97,151],"of":[6,18,36,52,72,79,94,98,113,121,130,147,152],"rational":[7],"polyhedra":[8,80,99],"whose":[9],"integer":[10,29,47],"points":[11,30,48],"are":[12,100,105,124],"in":[13,31,143],"bijection":[14,32],"with":[15,33,55],"certain":[16],"numerical":[19,34,53,155],"semigroups.":[20],"One":[21],"such":[22],"family,":[23],"first":[24],"introduced":[25,41],"by":[26,42,127],"Kunz,":[27],"has":[28,46],"semigroups":[35,54,141],"fixed":[37],"multiplicity,":[38],"and":[39,44,133],"another,":[40],"Hellus":[43],"Waldi,":[45],"corresponding":[49,145],"to":[50,68,108,140],"oversemigroups":[51],"two":[56,150],"generators.":[57],"In":[58],"this":[59,136],"paper,":[60],"we":[61],"provide":[62],"a":[63,76,111,128],"combinatorial":[64,137],"framework":[65],"from":[66,86,91,110],"which":[67,92],"study":[69,109],"both":[70,93],"polyhedra.":[73],"We":[74,116],"introduce":[75],"new":[77],"family":[78,129],"called":[81],"group":[82,122],"cones,":[83],"each":[84],"constructed":[85],"some":[87],"finite":[88,131],"abelian":[89],"group,":[90],"the":[95,119,144,148],"aforementioned":[96],"directly":[101],"determined":[102],"but":[103],"that":[104,118],"more":[106],"natural":[107],"standpoint":[112],"polyhedral":[114],"geometry.":[115],"prove":[117],"faces":[120,146],"cones":[123],"naturally":[125],"indexed":[126],"posets,":[132],"illustrate":[134],"how":[135],"data":[138],"relates":[139],"living":[142],"other":[149],"polyhedra.Keywords:":[153],"Polyhedron,":[154],"semigroup.Mathematics":[156],"Subject":[157],"Classifications:":[158],"52B05,":[159],"20M14":[160]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-28T14:05:53.105641","created_date":"2025-10-10T00:00:00"}