{"id":"https://openalex.org/W7135043449","doi":"https://doi.org/10.48550/arxiv.2603.10293","title":"Binomial Random Matroids","display_name":"Binomial Random Matroids","publication_year":2026,"publication_date":"2026-03-11","ids":{"openalex":"https://openalex.org/W7135043449","doi":"https://doi.org/10.48550/arxiv.2603.10293"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.10293","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.10293","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,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.10293","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5128814139","display_name":"Patrick Bennett","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bennett, Patrick","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5128846894","display_name":"Alan Frieze","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Frieze, Alan","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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.4275999963283539,"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"}},"topics":[{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.4275999963283539,"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"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.18129999935626984,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.08030000329017639,"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/matroid","display_name":"Matroid","score":0.9417999982833862},{"id":"https://openalex.org/keywords/event","display_name":"Event (particle physics)","score":0.5957000255584717},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5343000292778015},{"id":"https://openalex.org/keywords/binomial","display_name":"Binomial (polynomial)","score":0.5212000012397766},{"id":"https://openalex.org/keywords/greedy-algorithm","display_name":"Greedy algorithm","score":0.5045999884605408},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.47029998898506165}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.9417999982833862},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7275000214576721},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7231000065803528},{"id":"https://openalex.org/C2779662365","wikidata":"https://www.wikidata.org/wiki/Q5416694","display_name":"Event (particle physics)","level":2,"score":0.5957000255584717},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5343000292778015},{"id":"https://openalex.org/C2781315470","wikidata":"https://www.wikidata.org/wiki/Q193623","display_name":"Binomial (polynomial)","level":2,"score":0.5212000012397766},{"id":"https://openalex.org/C51823790","wikidata":"https://www.wikidata.org/wiki/Q504353","display_name":"Greedy algorithm","level":2,"score":0.5045999884605408},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4952000081539154},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.47029998898506165},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.3603000044822693},{"id":"https://openalex.org/C41054675","wikidata":"https://www.wikidata.org/wiki/Q185547","display_name":"Binomial distribution","level":2,"score":0.3287000060081482},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.3082999885082245},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.289000004529953},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.2824999988079071},{"id":"https://openalex.org/C22425182","wikidata":"https://www.wikidata.org/wiki/Q6787906","display_name":"Matroid partitioning","level":4,"score":0.28049999475479126}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.10293","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.10293","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,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.10293","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.10293","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,"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"},"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":{"Let":[0,22],"$\\mathcal":[1,30,94],"B=\\mathcal":[2],"B_{k,n,p}$":[3],"be":[4,26,197],"a":[5,38,64,75,97,105,110,115],"random":[6,111],"collection":[7,116],"of":[8,10,35,37,69,82,117,145,154,187,198],"$k$-subsets":[9],"$[n]$":[11],"where":[12,47,134],"each":[13],"possible":[14],"set":[15,34],"is":[16],"present":[17],"independently":[18],"with":[19,167,171,192],"probability":[20],"$p$.":[21],"$\\cal":[23,70,83,90],"E_{\\mathcal":[24,91],"B}$":[25,72,92],"the":[27,33,67,80,124,143,185],"event":[28],"that":[29,42,88,108,163],"B$":[31,95],"defines":[32,96],"bases":[36],"matroid.":[39],"We":[40,85,119],"prove":[41,74,87],"If":[43],"$p=":[44],"1-\\frac{c_n}{(k(n-k)\\binom":[45],"nk)^{1/2}}$":[46],"$0\\leq":[48],"c_n\\leq":[49],"\\infty$,":[50],"then":[51],"\\[":[52],"\\lim_{n\\to\\infty}\\Pr[\\cal":[53],"E_{\\cal":[54,71],"B}\\mid":[55],"|\\cal":[56],"B|\\geq2]=\\begin{cases}1&c_n\\to0.\\\\e^{-c^2/2}&c_n\\to":[57],"c.\\\\0&c_n\\to":[58],"\\infty.\\end{cases}\\]":[59],"In":[60,102],"addition,":[61,103],"we":[62,164,181],"identify":[63],"condition":[65],"preventing":[66],"occurence":[68,81],"and":[73,149],"hitting":[76],"time":[77],"version":[78],"for":[79,184],"B$.":[84],"also":[86],"when":[89],"occurs,":[93],"sparse":[98,150],"paving":[99,147,151],"matroid":[100,112],"w.h.p.":[101],"study":[104],"greedy":[106],"algorithm":[107],"produces":[109],"defined":[113],"by":[114],"hyperplanes.":[118],"use":[120],"this":[121],"to":[122,175],"improve":[123],"estimates":[125,183],"in":[126,162,177,189],"\\cite{HPV}":[127],"on":[128,157],"$\\log":[129],"m(n,k),\\log":[130],"p(n,k),":[131],"\\log":[132],"s(n,k)$":[133],"$":[135],"m(n,":[136],"k),":[137,139],"p(n,":[138],"s(n,":[140],"k)$":[141],"denote":[142],"number":[144,186],"matroids,":[146,148],"matroids":[152],"(respectively)":[153],"rank":[155],"$k$":[156,168],"$[n]$.":[158],"Our":[159],"improvement":[160],"lies":[161],"can":[165],"deal":[166],"growing":[169],"slowly":[170],"$n$":[172],"as":[173],"opposed":[174],"$k=O(1)$":[176],"\\cite{HPV}.":[178],"More":[179],"generally,":[180],"obtain":[182],"matchings":[188],"nearly-regular":[190],"hypergraphs":[191],"small":[193],"codegree,":[194],"which":[195],"may":[196],"independent":[199],"interest.":[200]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-03-13T00:00:00"}