{"id":"https://openalex.org/W7213580501","doi":"https://doi.org/10.48550/arxiv.2609.20726","title":"Extremal numbers of acyclic matrices","display_name":"Extremal numbers of acyclic matrices","publication_year":2026,"publication_date":"2026-09-17","ids":{"openalex":"https://openalex.org/W7213580501","doi":"https://doi.org/10.48550/arxiv.2609.20726"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.20726","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20726","pdf_url":"https://arxiv.org/pdf/2609.20726","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/2609.20726","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084893376","display_name":"Lior Gishboliner","orcid":"https://orcid.org/0000-0003-0688-8111","observed_orcids":["https://orcid.org/0000-0003-0688-8111"]},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Gishboliner, Lior","raw_affiliation_strings":["Department of Mathematics , University of Toronto , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Toronto , Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001033117","display_name":"Xiangyu Li","orcid":"https://orcid.org/0000-0002-1480-3686","observed_orcids":["https://orcid.org/0000-0002-1480-3686"]},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Li, Xiangyu","raw_affiliation_strings":["Department of Mathematics , University of Toronto , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Toronto , Canada","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I185261750"],"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":0.9613999724388123,"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":0.9613999724388123,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.03669999912381172,"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":0.000699999975040555,"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/extremal-number","display_name":"extremal number","score":0.7799999713897705},{"id":"https://openalex.org/keywords/zero-one-matrices","display_name":"zero-one matrices","score":0.8730000257492065},{"id":"https://openalex.org/keywords/forbidden-submatrices","display_name":"forbidden submatrices","score":0.6809999942779541},{"id":"https://openalex.org/keywords/extremal-graph-theory","display_name":"extremal graph theory","score":0.8629999756813049}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.633899986743927},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5799000263214111},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5393999814987183},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42179998755455017},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3488999903202057},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.2687999904155731},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.26080000400543213},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.25920000672340393},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.25540000200271606},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.25429999828338623}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.20726","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20726","pdf_url":"https://arxiv.org/pdf/2609.20726","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.2609.20726","doi":"https://doi.org/10.48550/arxiv.2609.20726","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.20726","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.20726","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20726","pdf_url":"https://arxiv.org/pdf/2609.20726","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":[{"id":"https://openalex.org/F4320322015","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213580501.pdf","grobid_xml":"https://content.openalex.org/works/W7213580501.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4382619305","https://openalex.org/W6891290363","https://openalex.org/W4415991582","https://openalex.org/W2012236087","https://openalex.org/W3121055929","https://openalex.org/W1482320371","https://openalex.org/W2080876227","https://openalex.org/W2966158295","https://openalex.org/W2069400461","https://openalex.org/W2797580864"],"abstract_inverted_index":{"For":[0],"a":[1],"zero-one":[2,17],"matrix":[3,18],"$P$,":[4,31],"let":[5],"$\\operatorname{Ex}(n,P)$":[6],"denote":[7],"the":[8,33,37],"maximum":[9],"number":[10],"of":[11,36],"ones":[12],"in":[13],"an":[14],"$n\\times":[15],"n$":[16],"avoiding":[19],"$P$.":[20],"We":[21],"prove":[22],"that":[23],"$$\\operatorname{Ex}(n,P)":[24],"\\leq":[25],"n^{1+O_P(1/\\log\\log":[26],"n)}$$":[27],"for":[28],"every":[29],"acyclic":[30],"settling":[32],"weak":[34],"form":[35],"Pach-Tardos":[38],"conjecture.":[39]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-19T00:00:00"}
