{"id":"https://openalex.org/W7214095010","doi":"https://doi.org/10.48550/arxiv.2609.26133","title":"A rate for the average vacancy of uniformly random matchings in linear hypergraphs","display_name":"A rate for the average vacancy of uniformly random matchings in linear hypergraphs","publication_year":2026,"publication_date":"2026-08-10","ids":{"openalex":"https://openalex.org/W7214095010","doi":"https://doi.org/10.48550/arxiv.2609.26133"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.26133","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26133","pdf_url":"https://arxiv.org/pdf/2609.26133","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.26133","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152555938","display_name":"Anish Gupta","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gupta, Anish","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5152555938"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9984999895095825,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9984999895095825,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.00039999998989515007,"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":0.00039999998989515007,"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/matching","display_name":"matching","score":0.49900001287460327},{"id":"https://openalex.org/keywords/linear-hypergraphs","display_name":"linear hypergraphs","score":0.9340000152587891},{"id":"https://openalex.org/keywords/asymptotic-enumeration","display_name":"asymptotic enumeration","score":0.5479999780654907},{"id":"https://openalex.org/keywords/edge-sampling","display_name":"edge sampling","score":0.4880000054836273},{"id":"https://openalex.org/keywords/hypergraph-matching","display_name":"hypergraph matching","score":0.4230000078678131}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8561000227928162},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.8388000130653381},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7437000274658203},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.6496999859809875},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5627999901771545},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.524399995803833},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.476500004529953},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.39169999957084656},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.3571999967098236},{"id":"https://openalex.org/C141042865","wikidata":"https://www.wikidata.org/wiki/Q200125","display_name":"Expected value","level":2,"score":0.29760000109672546},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.28999999165534973},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.26030001044273376},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.2529999911785126},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.2522999942302704}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.26133","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26133","pdf_url":"https://arxiv.org/pdf/2609.26133","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.26133","doi":"https://doi.org/10.48550/arxiv.2609.26133","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.26133","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.26133","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26133","pdf_url":"https://arxiv.org/pdf/2609.26133","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214095010.pdf","grobid_xml":"https://content.openalex.org/works/W7214095010.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1971289435","https://openalex.org/W1999344551","https://openalex.org/W2002707254","https://openalex.org/W2067142590","https://openalex.org/W2157827214","https://openalex.org/W2199658097","https://openalex.org/W2477838339","https://openalex.org/W3092384090","https://openalex.org/W4399596963","https://openalex.org/W4416344352","https://openalex.org/W7135043449"],"related_works":["https://openalex.org/W4399596963","https://openalex.org/W1809515066","https://openalex.org/W7222156038","https://openalex.org/W2967508960","https://openalex.org/W2002707254","https://openalex.org/W2050666090","https://openalex.org/W2326817677","https://openalex.org/W2982833457","https://openalex.org/W2104183200","https://openalex.org/W7098317321"],"abstract_inverted_index":{"Let":[0],"$M$":[1],"be":[2,18],"chosen":[3],"uniformly":[4,46],"from":[5,165],"all":[6],"matchings":[7,71],"of":[8,72,109,119],"a":[9,23,106,172],"finite":[10],"linear":[11],"$k$-uniform":[12],"hypergraph":[13],"$H$,":[14,105],"and":[15,34,45,67,89,121,157,162],"let":[16],"$\\overline{q}(H)$":[17],"the":[19,48,59,92,98,110,116,124,166],"average":[20,36],"probability":[21],"that":[22],"vertex":[24],"is":[25,58],"left":[26],"uncovered.":[27],"If":[28],"$H$":[29],"has":[30],"maximum":[31],"degree":[32,37],"$D$":[33],"normalized":[35],"$\u03b2=k|E(H)|/(|V(H)|D)$,":[38],"then,":[39],"for":[40,126,145],"every":[41,127],"fixed":[42,128],"$k\\geq":[43,129,146],"2$":[44],"in":[47],"order,":[49],"$\\overline{q}(H)":[50],"\\leq":[51,133],"1-\u03b2+(\u03b2k+o_D(1))\\log\\log":[52],"D/\\log":[53],"D$.":[54],"The":[55,148],"underlying":[56],"estimate":[57],"order-uniform":[60],"count":[61],"$\\log":[62],"Z(H)\\geq":[63],"(|E(H)|/D)(\\log":[64],"D-(k+o_D(1))\\log\\log":[65],"D)$,":[66],"it":[68],"also":[69,163],"counts":[70],"size":[73],"$(1-o_D(1))|E(H)|/D$.":[74],"We":[75],"prove":[76],"this":[77],"by":[78,143,155],"sampling":[79],"edges,":[80],"deleting":[81],"those":[82],"incident":[83],"with":[84],"unusually":[85],"large":[86],"sampled":[87],"degrees,":[88],"controlling":[90],"only":[91],"total":[93],"deleted":[94],"mass":[95],"before":[96],"applying":[97],"Molloy-Reed":[99],"list":[100],"edge-colouring":[101],"theorem.":[102],"For":[103],"$d$-regular":[104],"quantitative":[107],"version":[108],"earlier":[111],"Asratian-Kuzjurin":[112],"sampling-to-counting":[113],"route,":[114],"using":[115],"near-perfect-matching":[117],"theorem":[118],"Gould":[120],"Kelly,":[122],"sharpens":[123],"coefficient:":[125],"3$,":[130],"$\\sup_H":[131],"\\overline{q}(H)":[132],"(\\max\\{3,k-1\\}+o_d(1))\\log\\log":[134],"d/\\log":[135],"d$.":[136],"Kahn's":[137],"stronger":[138],"pointwise":[139],"prediction":[140],"was":[141,152],"disproved":[142],"Lee":[144],"3$.":[147],"qualitative":[149],"averaged":[150],"conclusion":[151],"already":[153],"recorded":[154],"Kahn":[156],"Kim,":[158],"crediting":[159],"Anders":[160],"Johansson,":[161],"follows":[164],"Grable-Asratian-Kuzjurin":[167],"enumeration;":[168],"neither":[169],"source":[170],"states":[171],"rate.":[173]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-24T00:00:00"}
