{"id":"https://openalex.org/W7165793717","doi":"https://doi.org/10.48550/arxiv.2606.24529","title":"An Erd\u0151s Matching Conjecture for Vector Spaces","display_name":"An Erd\u0151s Matching Conjecture for Vector Spaces","publication_year":2026,"publication_date":"2026-06-23","ids":{"openalex":"https://openalex.org/W7165793717","doi":"https://doi.org/10.48550/arxiv.2606.24529"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.24529","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.24529","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":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.24529","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5139287124","display_name":"Baoyan Feng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Feng, Baoyan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022619695","display_name":"Chong Shangguan","orcid":"https://orcid.org/0000-0002-3206-3968"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shangguan, Chong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138336549","display_name":"Yulin Yang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Yulin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5139243164","display_name":"Chenyang Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Chenyang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.29269999265670776,"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":0.29269999265670776,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.2531000077724457,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.09350000321865082,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/linear-subspace","display_name":"Linear subspace","score":0.7281000018119812},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.6485999822616577},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.6435999870300293},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6287999749183655},{"id":"https://openalex.org/keywords/matroid","display_name":"Matroid","score":0.5810999870300293},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5282999873161316},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.46000000834465027},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.41659998893737793}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8300999999046326},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.7281000018119812},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.6485999822616577},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.6435999870300293},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6287999749183655},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6122000217437744},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.5810999870300293},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5282999873161316},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5113000273704529},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.46000000834465027},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.41659998893737793},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4163999855518341},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.3221000134944916},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.29670000076293945},{"id":"https://openalex.org/C171739935","wikidata":"https://www.wikidata.org/wiki/Q726210","display_name":"Normed vector space","level":2,"score":0.29440000653266907},{"id":"https://openalex.org/C2780861221","wikidata":"https://www.wikidata.org/wiki/Q913849","display_name":"Minimax theorem","level":3,"score":0.2849999964237213},{"id":"https://openalex.org/C2776055716","wikidata":"https://www.wikidata.org/wiki/Q7316893","display_name":"Retract","level":2,"score":0.2784000039100647},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2777000069618225},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.2728999853134155},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.26179999113082886}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.24529","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.24529","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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.24529","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.24529","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":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,86],"study":[1],"a":[2,17,52,64,109,123,153,157,178],"vector-space":[3,74,110],"analogue":[4,75,111],"of":[5,16,19,22,47,59,76,112,160],"the":[6,13,56,72,77,102,113,117,128,165],"Erd\u0151s":[7,78],"Matching":[8,79],"Conjecture.":[9],"Let":[10],"$m_q(n,k,s)$":[11],"denote":[12],"maximum":[14],"cardinality":[15],"family":[18],"$k$-dimensional":[20],"subspaces":[21],"an":[23],"$n$-dimensional":[24],"vector":[25,144,189],"space":[26],"over":[27],"$\\mathbb":[28],"F_q$":[29],"with":[30,132,140],"no":[31],"$s+1$":[32],"members":[33],"whose":[34],"sum":[35],"is":[36,97],"direct.":[37],"Two":[38],"natural":[39],"constructions":[40,70],"provide":[41],"lower":[42],"bounds.":[43],"The":[44,169],"first":[45],"consists":[46,58],"all":[48,60,82],"$k$-subspaces":[49,61],"contained":[50],"in":[51,143,188],"fixed":[53,65],"$((s+1)k-1)$-dimensional":[54],"subspace;":[55],"second":[57],"that":[62],"intersect":[63],"$s$-dimensional":[66],"subspace":[67],"nontrivially.":[68],"These":[69],"motivate":[71],"following":[73],"Conjecture:":[80],"for":[81,164,175,182],"$n\\ge":[83],"(s+1)k$,":[84],"$$m_q(n,k,s)=\\max\\left\\{\\genfrac{[}{]}{0pt}{}{(s+1)k-1}{k}_q,~\\genfrac{[}{]}{0pt}{}{n}{k}_q-q^{ks}\\genfrac{[}{]}{0pt}{}{n-s}{k}_q\\right\\}.$$":[85],"prove":[87,122],"this":[88,133,138],"conjecture":[89],"when":[90,92,95],"$k=2$,":[91],"$n=(s+1)k$,":[93],"and":[94,146,162,185],"$n$":[96],"sufficiently":[98],"large.":[99],"In":[100,116],"particular,":[101],"case":[103,167],"$k=2$":[104],"may":[105],"be":[106],"viewed":[107],"as":[108],"Erd\u0151s--Gallai":[114],"theorem.":[115],"large-$n$":[118],"range,":[119],"we":[120,136],"also":[121],"Hilton--Milner-type":[124],"stability":[125],"theorem,":[126],"determining":[127],"largest":[129],"nontrivial":[130],"families":[131,142],"property.":[134],"Finally,":[135],"connect":[137],"problem":[139],"$t$-cover-free":[141],"spaces":[145],"determine":[147],"their":[148],"extremal":[149],"number":[150],"up":[151],"to":[152],"lower-order":[154],"term,":[155],"extending":[156],"recent":[158],"result":[159],"Shan":[161],"Zhou":[163],"special":[166],"$t=2$.":[168],"proofs":[170],"combine":[171],"Lov\u00e1sz's":[172],"minimax":[173],"theorem":[174],"matroid":[176],"matchings,":[177],"high-dimensional":[179],"Hoffman":[180],"bound":[181],"uniform":[183],"hypergraphs,":[184],"packing-design":[186],"arguments":[187],"spaces.":[190]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-25T00:00:00"}