{"id":"https://openalex.org/W7222395934","doi":"https://doi.org/10.48550/arxiv.2610.22082","title":"Integral homology lattices of matching and circulant complexes","display_name":"Integral homology lattices of matching and circulant complexes","publication_year":2026,"publication_date":"2026-10-15","ids":{"openalex":"https://openalex.org/W7222395934","doi":"https://doi.org/10.48550/arxiv.2610.22082"},"language":"en","primary_location":{"id":"doi:10.48550/arxiv.2610.22082","doi":"https://doi.org/10.48550/arxiv.2610.22082","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.22082","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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2610.22082","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158912881","display_name":"Qihang Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wang, Qihang","raw_affiliation_strings":["School of Mathematical Sciences , Peking University , Beijing 100871 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , Peking University , Beijing 100871 , China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039313397","display_name":"Weiye Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li, Weiye","raw_affiliation_strings":["Department of Automation , Tsinghua University , Beijing 100084 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Automation , Tsinghua University , Beijing 100084 , China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.4683000147342682,"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"}},"topics":[{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.4683000147342682,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.46389999985694885,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.033799998462200165,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/independence-complexes","display_name":"independence complexes","score":0.7450000047683716},{"id":"https://openalex.org/keywords/homotopy-classification","display_name":"homotopy classification","score":0.847000002861023}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8669000267982483},{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.6200000047683716},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.5849000215530396},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.48030000925064087},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43209999799728394},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.415800005197525},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.39800000190734863},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38339999318122864},{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.335999995470047},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.3212999999523163},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30489999055862427},{"id":"https://openalex.org/C79536532","wikidata":"https://www.wikidata.org/wiki/Q1959911","display_name":"Relative homology","level":3,"score":0.3034000098705292},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C55537702","wikidata":"https://www.wikidata.org/wiki/Q3139849","display_name":"Cellular homology","level":3,"score":0.2712000012397766},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C89025888","wikidata":"https://www.wikidata.org/wiki/Q911907","display_name":"Dihedral angle","level":4,"score":0.257099986076355}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2610.22082","doi":"https://doi.org/10.48550/arxiv.2610.22082","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.22082","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":"doi:10.48550/arxiv.2610.22082","doi":"https://doi.org/10.48550/arxiv.2610.22082","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.22082","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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7204144516","https://openalex.org/W2087202577","https://openalex.org/W7204946360","https://openalex.org/W7098126705","https://openalex.org/W2086254793","https://openalex.org/W2001690459","https://openalex.org/W7100651426","https://openalex.org/W2139771308","https://openalex.org/W7095279911","https://openalex.org/W2884990022"],"abstract_inverted_index":{"Bouc's":[0],"hook":[1,48],"cycles":[2,32],"span":[3],"the":[4,9,38,45,59,77,87],"rational":[5,158],"top":[6],"homology":[7,39,62,103,108],"of":[8,12,64,81],"matching":[10],"complex":[11],"$K_{2k+1}$.":[13],"We":[14],"prove":[15,131],"that":[16],"their":[17],"integral":[18,47,60],"saturation":[19,114],"quotient":[20],"has":[21],"exponent":[22],"exactly":[23],"$2^{\\lfloor":[24],"k/2\\rfloor}$":[25],"for":[26,69],"every":[27,146],"$k\\geq1$,":[28],"and":[29,67,72,75,93,128,137],"construct":[30],"divided-power":[31],"attaining":[33],"this":[34],"bound.":[35],"For":[36,54,121,145],"$k\\geq2$,":[37],"lattice":[40,49],"is":[41],"not":[42],"isomorphic":[43],"to":[44,86,101,118,141],"standard":[46],"as":[50],"an":[51,132],"$\\mathfrak":[52],"S_{2k+1}$-module.":[53],"circulant":[55,122],"complexes,":[56],"we":[57,130],"determine":[58],"dihedral":[61],"modules":[63],"$\\operatorname{Ind}(C_{3s}^{s-1})$,":[65],"$\\operatorname{Ind}(C_{3s+1}^{s-1})$":[66],"$\\operatorname{Ind}(C_{3s+2}^{s-1})$,":[68],"$s\\geq3$,":[70,73],"$s\\geq2$":[71],"respectively,":[74],"classify":[76],"least":[78],"scalar":[79],"lifts":[80],"all":[82],"primitive":[83],"equivariant":[84,119],"quotients":[85],"rank-one":[88],"module":[89],"with":[90,125],"trivial":[91],"rotation":[92],"negative":[94],"reflection.":[95],"Tate":[96],"localization":[97],"relates":[98],"prime-order":[99],"gluing":[100],"fixed-point":[102],"under":[104],"a":[105,138,153,157],"free,":[106],"single-degree":[107],"hypothesis.":[109],"Explicit":[110],"cycle":[111],"subgroups":[112],"separate":[113],"defects":[115],"from":[116],"obstructions":[117],"sections.":[120],"independence":[123],"complexes":[124],"jumps":[126],"two":[127],"three,":[129],"eight-periodic":[133],"ordinary":[134],"homotopy":[135],"classification":[136],"fixed-space":[139],"obstruction":[140],"uniform":[142],"representation":[143],"suspensions.":[144],"fixed":[147],"nonempty":[148],"bounded":[149],"positive":[150],"jump":[151],"set,":[152],"finite-state":[154],"construction":[155],"gives":[156],"critical-face":[159],"series.":[160]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-17T00:00:00"}