{"id":"https://openalex.org/W7225185029","doi":"https://doi.org/10.48550/arxiv.2611.03261","title":"Exact Agreement Expansion up to the Top via Non-polarity","display_name":"Exact Agreement Expansion up to the Top via Non-polarity","publication_year":2026,"publication_date":"2026-11-02","ids":{"openalex":"https://openalex.org/W7225185029","doi":"https://doi.org/10.48550/arxiv.2611.03261"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2611.03261","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.03261","pdf_url":"https://arxiv.org/pdf/2611.03261","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2611.03261","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109110331","display_name":"Tali Kaufman","orcid":"https://orcid.org/0009-0009-6776-8763","observed_orcids":["https://orcid.org/0009-0009-6776-8763"]},"institutions":[{"id":"https://openalex.org/I13955877","display_name":"Bar-Ilan University","ror":"https://ror.org/03kgsv495","country_code":"IL","type":"education","lineage":["https://openalex.org/I13955877"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Kaufman, Tali","raw_affiliation_strings":["Department of Computer Science and Artificial Intelligence Bar - Ilan University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Artificial Intelligence Bar - Ilan University","institution_ids":["https://openalex.org/I13955877"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060274649","display_name":"Huy Tuan Pham","orcid":"https://orcid.org/0000-0003-4659-4345","observed_orcids":["https://orcid.org/0000-0003-4659-4345"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pham, Huy Tuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"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":0.41499999165534973,"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":0.41499999165534973,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.4120999872684479,"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":0.05480000004172325,"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/simplicial-complex","display_name":"simplicial complexes","score":0.9509999752044678},{"id":"https://openalex.org/keywords/matroid-bases","display_name":"matroid bases","score":0.8080000281333923},{"id":"https://openalex.org/keywords/independent-sets","display_name":"independent sets","score":0.7390000224113464},{"id":"https://openalex.org/keywords/soundness","display_name":"soundness","score":0.5630000233650208}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6639999747276306},{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.6229000091552734},{"id":"https://openalex.org/C162929932","wikidata":"https://www.wikidata.org/wiki/Q129638","display_name":"Grassmannian","level":2,"score":0.6165000200271606},{"id":"https://openalex.org/C186080144","wikidata":"https://www.wikidata.org/wiki/Q358733","display_name":"Series expansion","level":2,"score":0.5332000255584717},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42719998955726624},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.4230000078678131},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.41929998993873596},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3935999870300293},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.3903000056743622},{"id":"https://openalex.org/C2985906921","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Spectral properties","level":2,"score":0.37790000438690186},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.3752000033855438},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.34540000557899475},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3407000005245209},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.2816999852657318},{"id":"https://openalex.org/C2779304628","wikidata":"https://www.wikidata.org/wiki/Q3503480","display_name":"Face (sociological concept)","level":2,"score":0.2815999984741211},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.26930001378059387},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.257999986410141},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2526000142097473},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2611.03261","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.03261","pdf_url":"https://arxiv.org/pdf/2611.03261","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.2611.03261","doi":"https://doi.org/10.48550/arxiv.2611.03261","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2611.03261","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:2611.03261","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.03261","pdf_url":"https://arxiv.org/pdf/2611.03261","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/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7225185029.pdf","grobid_xml":"https://content.openalex.org/works/W7225185029.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3003633209","https://openalex.org/W2972287267","https://openalex.org/W4414080979","https://openalex.org/W4399523655","https://openalex.org/W3128760565","https://openalex.org/W4320169773","https://openalex.org/W4386044060","https://openalex.org/W2730345043","https://openalex.org/W4404849183","https://openalex.org/W2730015764"],"abstract_inverted_index":{"Agreement":[0,29],"expansion":[1,30,54,58,70,83,96,108,112,143],"asks":[2],"whether":[3],"local":[4,35,189,203],"assignments":[5,36,86,102],"to":[6,38,87,103],"faces":[7,89],"of":[8,90,146,156,199,202,210],"a":[9,15,22,48,92,188,207],"poset":[10],"that":[11,55,153],"usually":[12],"agree":[13,20,41],"on":[14,26,85,177],"sampled":[16],"common":[17],"face":[18],"must":[19],"with":[21,42,163,184],"single":[23],"global":[24,44],"function":[25],"most":[27],"faces.":[28],"is":[31,97],"exact":[32,68,79,133,161,175],"(approximate)":[33],"if":[34],"need":[37],"exactly":[39],"(approximately)":[40],"the":[43,91,200],"function.":[45],"We":[46,172],"suggest":[47],"new":[49],"proof":[50,194],"technique":[51],"for":[52,71,101,124],"agreement":[53,57,69,80,82,95,107,134,162,176],"enables":[56],"in":[59,120,144],"settings":[60],"which":[61],"were":[62],"previously":[63],"beyond":[64],"reach,":[65],"such":[66],"as:":[67],"Grassmannian":[72,128,178],"posets":[73,179],"(before":[74,94],"only":[75,100],"simplicial":[76,126],"complexes":[77],"support":[78],"expansion);":[81],"based":[84],"top":[88],"complex":[93],"generally":[98],"proven":[99],"low":[104],"dimensional":[105],"faces);":[106],"from":[109],"one-sided":[110,141,181],"spectral":[111,116,142,182],"(before,":[113],"two":[114,138],"sided":[115],"assumption":[117],"was":[118],"needed":[119],"general":[121],"settings).":[122],"Specifically,":[123],"down-closed":[125],"and":[127],"complexes,":[129],"we":[130,151],"prove":[131],"an":[132,149],"theorem":[135],"between":[136],"any":[137],"layers":[139],"assuming":[140],"links":[145],"singletons.":[147],"As":[148],"application,":[150],"show":[152],"full":[154],"bases":[155],"every":[157],"rank-$k$":[158],"matroid":[159],"admit":[160],"soundness":[164,186],"$O(k^2/[h(k-h)])$":[165],"when":[166],"tested":[167],"through":[168],"$h$-element":[169],"independent":[170],"sets.":[171],"also":[173],"obtain":[174],"under":[180,187],"expansion,":[183],"stronger":[185],"distance":[190],"guarantee.":[191],"Our":[192],"key":[193],"ideas":[195],"center":[196],"around":[197],"non-polarity":[198],"distributions":[201],"assignments,":[204],"probed":[205],"via":[206],"random":[208],"exposure":[209],"elements.":[211]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-11-04T00:00:00"}
