{"id":"https://openalex.org/W2968435267","doi":"https://doi.org/10.1017/s0963548321000122","title":"Counting matchings via capacity-preserving operators","display_name":"Counting matchings via capacity-preserving operators","publication_year":2021,"publication_date":"2021-04-30","ids":{"openalex":"https://openalex.org/W2968435267","doi":"https://doi.org/10.1017/s0963548321000122","mag":"2968435267"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548321000122","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548321000122","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9CF63D280E8003E749CEE81A9C2859C7/S0963548321000122a.pdf/div-class-title-counting-matchings-via-capacity-preserving-operators-div.pdf","source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9CF63D280E8003E749CEE81A9C2859C7/S0963548321000122a.pdf/div-class-title-counting-matchings-via-capacity-preserving-operators-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022317936","display_name":"Leonid Gurvits","orcid":"https://orcid.org/0000-0002-0694-2459"},"institutions":[{"id":"https://openalex.org/I125687163","display_name":"City College of New York","ror":"https://ror.org/00wmhkr98","country_code":"US","type":"education","lineage":["https://openalex.org/I125687163"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Leonid Gurvits","raw_affiliation_strings":["City College of New York, New York, NY, USA"],"affiliations":[{"raw_affiliation_string":"City College of New York, New York, NY, USA","institution_ids":["https://openalex.org/I125687163"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051294838","display_name":"Jonathan Leake","orcid":null},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Jonathan Leake","raw_affiliation_strings":["KTH, Stockholm, Sweden"],"affiliations":[{"raw_affiliation_string":"KTH, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5051294838"],"corresponding_institution_ids":["https://openalex.org/I86987016"],"apc_list":null,"apc_paid":null,"fwci":0.4206,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.53616239,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"30","issue":"6","first_page":"956","last_page":"981"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9995999932289124,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9994000196456909,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.715576171875},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.7145910859107971},{"id":"https://openalex.org/keywords/matroid","display_name":"Matroid","score":0.6670428514480591},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6249980926513672},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5902248024940491},{"id":"https://openalex.org/keywords/van-der-waerdens-theorem","display_name":"Van der Waerden's theorem","score":0.58537358045578},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5843591690063477},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5747092366218567},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.5169210433959961},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.493814080953598},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.49088841676712036},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.45779237151145935},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4129228889942169},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14834558963775635},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.11326327919960022}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.715576171875},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.7145910859107971},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.6670428514480591},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6249980926513672},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5902248024940491},{"id":"https://openalex.org/C116493835","wikidata":"https://www.wikidata.org/wiki/Q764287","display_name":"Van der Waerden's theorem","level":2,"score":0.58537358045578},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5843591690063477},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5747092366218567},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5169210433959961},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.493814080953598},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.49088841676712036},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.45779237151145935},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4129228889942169},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14834558963775635},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.11326327919960022},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1017/s0963548321000122","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548321000122","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9CF63D280E8003E749CEE81A9C2859C7/S0963548321000122a.pdf/div-class-title-counting-matchings-via-capacity-preserving-operators-div.pdf","source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1804.04351","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1804.04351","pdf_url":"https://arxiv.org/pdf/1804.04351","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:2968435267","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1804.04351","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.1804.04351","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1804.04351","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":"doi:10.1017/s0963548321000122","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548321000122","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9CF63D280E8003E749CEE81A9C2859C7/S0963548321000122a.pdf/div-class-title-counting-matchings-via-capacity-preserving-operators-div.pdf","source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2968435267.pdf","grobid_xml":"https://content.openalex.org/works/W2968435267.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1883732049","https://openalex.org/W1999344551","https://openalex.org/W2003979730","https://openalex.org/W2016724581","https://openalex.org/W2027584441","https://openalex.org/W2033114070","https://openalex.org/W2044544094","https://openalex.org/W2045842961","https://openalex.org/W2100552771","https://openalex.org/W2142658489","https://openalex.org/W2144476110","https://openalex.org/W2148195034","https://openalex.org/W2150949626","https://openalex.org/W2152309892","https://openalex.org/W2155237361","https://openalex.org/W2157491291","https://openalex.org/W2158620240","https://openalex.org/W2160923591","https://openalex.org/W2563037975","https://openalex.org/W2593579637","https://openalex.org/W2963345594","https://openalex.org/W2964127965","https://openalex.org/W2964165785","https://openalex.org/W3036257878","https://openalex.org/W3123082523","https://openalex.org/W4254798858","https://openalex.org/W6657586711"],"related_works":["https://openalex.org/W3158861169","https://openalex.org/W2978226723","https://openalex.org/W1580013167","https://openalex.org/W2949915340","https://openalex.org/W76737142","https://openalex.org/W2290305099","https://openalex.org/W2902035538","https://openalex.org/W2547088347","https://openalex.org/W3113169728","https://openalex.org/W2949884361","https://openalex.org/W2575486454","https://openalex.org/W2912441791","https://openalex.org/W3111799105","https://openalex.org/W2953331499","https://openalex.org/W2405333517","https://openalex.org/W2753377943","https://openalex.org/W2799781558","https://openalex.org/W2951914524","https://openalex.org/W1732373389","https://openalex.org/W1524380431"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"notion":[2,49],"of":[3,6,21,30,40,50,72,74,79,98,135,139],"the":[4,22,48,70,96,107],"capacity":[5,51,97,116],"a":[7,75,90,99,132,136],"polynomial":[8],"was":[9],"introduced":[10],"by":[11,84,113],"Gurvits":[12],"around":[13],"2005,":[14],"originally":[15],"to":[16,55,61,65,130],"give":[17,62,131],"drastically":[18],"simplified":[19],"proofs":[20],"van":[23],"der":[24],"Waerden":[25],"lower":[26,144],"bound":[27,56],"for":[28,37,119],"permanents":[29],"doubly":[31],"stochastic":[32],"matrices":[33],"and":[34,60],"Schrijver\u2019s":[35],"inequality":[36],"perfect":[38],"matchings":[39],"regular":[41],"bipartite":[42],"graphs.":[43],"Since":[44],"this":[45,103,128],"seminal":[46],"work,":[47],"has":[52],"been":[53],"utilised":[54],"various":[57],"combinatorial":[58],"quantities":[59,68],"polynomial-time":[63],"algorithms":[64],"approximate":[66],"such":[67,110],"(e.g.":[69],"number":[71],"bases":[73],"matroid).":[76],"These":[77],"types":[78],"results":[80],"are":[81],"often":[82],"proven":[83],"giving":[85,114],"bounds":[86,118],"on":[87],"how":[88],"much":[89],"particular":[91],"differential":[92],"operator":[93],"can":[94],"change":[95],"given":[100],"polynomial.":[101],"In":[102],"paper,":[104],"we":[105],"unify":[106],"theory":[108,129],"surrounding":[109],"capacity-preserving":[111],"operators":[112],"tight":[115],"preservation":[117],"all":[120],"nondegenerate":[121],"real":[122],"stability":[123],"preservers.":[124],"We":[125],"then":[126],"use":[127],"new":[133],"proof":[134],"recent":[137],"result":[138],"Csikv\u00e1ri,":[140],"which":[141],"settled":[142],"Friedland\u2019s":[143],"matching":[145],"conjecture.":[146]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
