{"id":"https://openalex.org/W7221836446","doi":"https://doi.org/10.48550/arxiv.2610.17798","title":"Lattice Bruhat intervals are polytopal","display_name":"Lattice Bruhat intervals are polytopal","publication_year":2026,"publication_date":"2026-10-13","ids":{"openalex":"https://openalex.org/W7221836446","doi":"https://doi.org/10.48550/arxiv.2610.17798"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.17798","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.17798","pdf_url":"https://arxiv.org/pdf/2610.17798","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/2610.17798","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158734005","display_name":"Yibo Gao","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gao, Yibo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5098809847","display_name":"Tao Gui","orcid":"https://orcid.org/0000-0002-6634-2420","observed_orcids":["https://orcid.org/0000-0002-6634-2420"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gui, Tao","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":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/T10948","display_name":"Advanced Combinatorial Mathematics","score":1.0,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":1.0,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.0,"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"}},{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.0,"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/coxeter-groups","display_name":"Coxeter groups","score":0.8949999809265137},{"id":"https://openalex.org/keywords/kazhdan-lusztig-polynomials","display_name":"Kazhdan-Lusztig polynomials","score":0.9769999980926514},{"id":"https://openalex.org/keywords/face-lattice","display_name":"face lattice","score":0.6029999852180481},{"id":"https://openalex.org/keywords/convex-polytopes","display_name":"convex polytopes","score":0.7459999918937683},{"id":"https://openalex.org/keywords/weyl-group","display_name":"Weyl group","score":0.9369999766349792},{"id":"https://openalex.org/keywords/richardson-varieties","display_name":"Richardson varieties","score":0.996999979019165},{"id":"https://openalex.org/keywords/intersection-cohomology","display_name":"intersection cohomology","score":0.8870000243186951},{"id":"https://openalex.org/keywords/m-sequences","display_name":"m-sequences","score":0.9269999861717224}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8392000198364258},{"id":"https://openalex.org/C177274530","wikidata":"https://www.wikidata.org/wiki/Q4978697","display_name":"Bruhat order","level":3,"score":0.7577000260353088},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.595300018787384},{"id":"https://openalex.org/C143669375","wikidata":"https://www.wikidata.org/wiki/Q7874246","display_name":"Coxeter group","level":2,"score":0.5827999711036682},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.5633000135421753},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5629000067710876},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.49050000309944153},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4440000057220459},{"id":"https://openalex.org/C40233952","wikidata":"https://www.wikidata.org/wiki/Q768074","display_name":"Weyl group","level":2,"score":0.3855000138282776},{"id":"https://openalex.org/C146922319","wikidata":"https://www.wikidata.org/wiki/Q4298935","display_name":"Schur polynomial","level":5,"score":0.3781000077724457},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36039999127388},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.35920000076293945},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.32269999384880066},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.314300000667572},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.30820000171661377},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30410000681877136},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.289000004529953},{"id":"https://openalex.org/C132170107","wikidata":"https://www.wikidata.org/wiki/Q834585","display_name":"Semilattice","level":3,"score":0.28839999437332153},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.2669999897480011}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.17798","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.17798","pdf_url":"https://arxiv.org/pdf/2610.17798","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.2610.17798","doi":"https://doi.org/10.48550/arxiv.2610.17798","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.17798","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":"pmh:oai:arXiv.org:2610.17798","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.17798","pdf_url":"https://arxiv.org/pdf/2610.17798","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":[{"id":"https://openalex.org/G8375472148","display_name":null,"funder_award_id":"12471309","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221836446.pdf","grobid_xml":"https://content.openalex.org/works/W7221836446.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W4417134194","https://openalex.org/W7123932483","https://openalex.org/W7147349323","https://openalex.org/W7212588582"],"related_works":["https://openalex.org/W2043377311","https://openalex.org/W1713122550","https://openalex.org/W1855451588","https://openalex.org/W2790137560","https://openalex.org/W2940900027","https://openalex.org/W2088518787","https://openalex.org/W2033822032","https://openalex.org/W2054001450","https://openalex.org/W7099390692","https://openalex.org/W2774871747"],"abstract_inverted_index":{"For":[0,77],"a":[1,12,16,20,31,54,63,109],"Bruhat":[2,43,56,79],"interval":[3,57],"$[x,y]$":[4],"in":[5,81],"an":[6,125],"arbitrary":[7],"Coxeter":[8],"group":[9],"which":[10],"is":[11],"lattice,":[13],"we":[14,85],"give":[15],"type-uniform":[17],"construction":[18],"of":[19,34,53,66,93,120],"convex":[21],"polytope":[22],"whose":[23],"complete":[24],"face":[25],"lattice":[26,42,55,78],"realizes":[27],"$[x,y]$.":[28],"This":[29],"gives":[30],"polytopal":[32],"realization":[33],"the":[35,50,70,87,90,118],"coincidence":[36],"between":[37],"classical":[38],"Kazhdan--Lusztig":[39,51,122],"polynomials":[40,123],"for":[41,75,99,112],"intervals":[44,80],"and":[45,68,96,102],"Stanley's":[46],"toric":[47,91],"$g$-polynomials.":[48],"Consequently,":[49],"polynomial":[52],"cannot":[58],"have":[59],"internal":[60],"zeros,":[61],"satisfies":[62],"multiplicative":[64],"strengthening":[65],"monotonicity,":[67],"obeys":[69],"generalized":[71],"upper":[72],"bound":[73],"theorem":[74],"polytopes.":[76],"finite":[82],"Weyl":[83],"groups,":[84],"explain":[86],"relation":[88],"with":[89],"geometry":[92],"Richardson":[94],"varieties":[95],"derive":[97],"formulas":[98],"their":[100],"local":[101],"global":[103],"intersection":[104],"cohomology,":[105],"as":[106,108],"well":[107],"Boolean":[110],"criterion":[111],"rational":[113],"smoothness.":[114],"We":[115],"conjecture":[116],"that":[117],"coefficients":[119],"these":[121],"form":[124],"$M$-sequence.":[126]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-15T00:00:00"}