{"id":"https://openalex.org/W2804761796","doi":"https://doi.org/10.1080/10586458.2021.1980455","title":"Number of Vertices of the Polytope of Integer Partitions and Factorization of the Partitioned Number","display_name":"Number of Vertices of the Polytope of Integer Partitions and Factorization of the Partitioned Number","publication_year":2021,"publication_date":"2021-10-22","ids":{"openalex":"https://openalex.org/W2804761796","doi":"https://doi.org/10.1080/10586458.2021.1980455","mag":"2804761796"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2021.1980455","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2021.1980455","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","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/A5053043997","display_name":"\u0412. \u0410. \u0428\u043b\u044b\u043a","orcid":"https://orcid.org/0000-0002-0869-3724"},"institutions":[{"id":"https://openalex.org/I291386647","display_name":"Belarusian State University","ror":"https://ror.org/021036w13","country_code":"BY","type":"education","lineage":["https://openalex.org/I291386647"]}],"countries":["BY"],"is_corresponding":true,"raw_author_name":"Vladimir A. Shlyk","raw_affiliation_strings":["Department of Mathematics and Mechanics, Belarusian State University, Minsk, Belarus"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Mechanics, Belarusian State University, Minsk, Belarus","institution_ids":["https://openalex.org/I291386647"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5053043997"],"corresponding_institution_ids":["https://openalex.org/I291386647"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00878294,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"32","issue":"3","first_page":"457","last_page":"466"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9990000128746033,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9986000061035156,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9036022424697876},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8731695413589478},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.6522983312606812},{"id":"https://openalex.org/keywords/convex-polytope","display_name":"Convex polytope","score":0.5578045845031738},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.5349869132041931},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5160526633262634},{"id":"https://openalex.org/keywords/polyhedral-combinatorics","display_name":"Polyhedral combinatorics","score":0.5140558481216431},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4578498899936676},{"id":"https://openalex.org/keywords/divisibility-rule","display_name":"Divisibility rule","score":0.4516172409057617},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35840415954589844},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3347657024860382},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.12662485241889954},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.089581698179245}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9036022424697876},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8731695413589478},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.6522983312606812},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.5578045845031738},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.5349869132041931},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5160526633262634},{"id":"https://openalex.org/C174248988","wikidata":"https://www.wikidata.org/wiki/Q8348314","display_name":"Polyhedral combinatorics","level":5,"score":0.5140558481216431},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4578498899936676},{"id":"https://openalex.org/C9991821","wikidata":"https://www.wikidata.org/wiki/Q858520","display_name":"Divisibility rule","level":2,"score":0.4516172409057617},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35840415954589844},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3347657024860382},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.12662485241889954},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.089581698179245},{"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},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10586458.2021.1980455","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2021.1980455","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5099999904632568,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1978661177","https://openalex.org/W1983127118","https://openalex.org/W1993760553","https://openalex.org/W2014306437","https://openalex.org/W2025915073","https://openalex.org/W2031149035","https://openalex.org/W2037238333","https://openalex.org/W2065803772","https://openalex.org/W2085460780","https://openalex.org/W2090340636","https://openalex.org/W2108822671","https://openalex.org/W2125838758","https://openalex.org/W2169153843","https://openalex.org/W2557830091","https://openalex.org/W2742395354","https://openalex.org/W2962774404","https://openalex.org/W2963721335","https://openalex.org/W2964192773","https://openalex.org/W3104617133"],"related_works":["https://openalex.org/W2098081711","https://openalex.org/W2056091804","https://openalex.org/W2079789648","https://openalex.org/W3105408998","https://openalex.org/W2557288725","https://openalex.org/W2768257653","https://openalex.org/W4288417334","https://openalex.org/W2069107464","https://openalex.org/W2137932663","https://openalex.org/W2045384787"],"abstract_inverted_index":{"The":[0,17],"polytope":[1,25,81],"of":[2,5,11,19,23,45,47,64,75,90,97,114,119,130,132],"integer":[3,15,76],"partitions":[4,46],"n":[6,65],"is":[7,99],"the":[8,12,21,24,32,42,95,112,128,133,138],"convex":[9,73],"hull":[10],"corresponding":[13,103],"n-dimensional":[14],"points.":[16,85],"graph":[18,96],"v(n),":[20],"number":[22,44,129],"vertices,":[26],"has":[27,141],"a":[28,87],"tooth-shaped":[29],"form":[30],"with":[31],"highest":[33],"peaks":[34],"at":[35],"primes.":[36],"We":[37,60,121],"explain":[38],"its":[39],"shape":[40],"by":[41,53,66],"large":[43],"even":[48],"n\u2019s":[49],"that":[50,62,94,111,127],"were":[51],"counted":[52],"N.":[54],"Metropolis":[55],"and":[56,71],"P.":[57],"R.":[58],"Stein.":[59],"reveal":[61],"divisibility":[63],"3":[67],"also":[68,122],"reduces":[69],"v(n)":[70,98,115],"characterize":[72],"representations":[74],"points":[77],"in":[78],"arbitrary":[79],"integral":[80],"via":[82],"three":[83],"other":[84],"Using":[86],"specific":[88],"classification":[89],"integers,":[91],"we":[92],"demonstrate":[93],"stratified":[100],"into":[101],"layers":[102],"to":[104],"resulting":[105],"classes.":[106],"Our":[107],"main":[108],"conjecture":[109],"claims":[110],"value":[113],"depends":[116],"on":[117,137],"factorization":[118],"n.":[120],"offer":[123],"an":[124],"argument":[125],"for":[126],"vertices":[131],"master":[134],"corner":[135],"polyhedron":[136],"cyclic":[139],"group":[140],"similar":[142],"features.":[143]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
