{"id":"https://openalex.org/W7212058965","doi":"https://doi.org/10.48550/arxiv.2609.08760","title":"Set-valued tableaux and cells of Gelfand-Zetlin polytopes","display_name":"Set-valued tableaux and cells of Gelfand-Zetlin polytopes","publication_year":2026,"publication_date":"2026-09-08","ids":{"openalex":"https://openalex.org/W7212058965","doi":"https://doi.org/10.48550/arxiv.2609.08760"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.08760","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.08760","pdf_url":"https://arxiv.org/pdf/2609.08760","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/2609.08760","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5122916693","display_name":"Evgeny Smirnov","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Smirnov, Evgeny","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5122916693"],"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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"}}],"keywords":[{"id":"https://openalex.org/keywords/cellular-decomposition","display_name":"cellular decomposition","score":0.7730000019073486},{"id":"https://openalex.org/keywords/bijections","display_name":"bijections","score":0.8119999766349792},{"id":"https://openalex.org/keywords/young-tableaux","display_name":"Young tableaux","score":0.515999972820282},{"id":"https://openalex.org/keywords/combinatorial-rules","display_name":"combinatorial rules","score":0.4449999928474426}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7850000262260437},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.775600016117096},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.7613000273704529},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7465000152587891},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.6492000222206116},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5960000157356262},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4781999886035919},{"id":"https://openalex.org/C162929932","wikidata":"https://www.wikidata.org/wiki/Q129638","display_name":"Grassmannian","level":2,"score":0.4602999985218048},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.415800005197525},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4106000065803528},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.38040000200271606},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.3546000123023987},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.3037000000476837},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.2996000051498413},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.263700008392334},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2628999948501587},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.2621000111103058},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.2619999945163727},{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.25679999589920044},{"id":"https://openalex.org/C2780130068","wikidata":"https://www.wikidata.org/wiki/Q2208651","display_name":"Transversal (combinatorics)","level":2,"score":0.25279998779296875}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.08760","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.08760","pdf_url":"https://arxiv.org/pdf/2609.08760","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.2609.08760","doi":"https://doi.org/10.48550/arxiv.2609.08760","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.08760","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:2609.08760","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.08760","pdf_url":"https://arxiv.org/pdf/2609.08760","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":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212058965.pdf","grobid_xml":"https://content.openalex.org/works/W7212058965.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W3130743169","https://openalex.org/W7052228230"],"related_works":["https://openalex.org/W2334499192","https://openalex.org/W4403975967","https://openalex.org/W3159407172","https://openalex.org/W4205473223","https://openalex.org/W2962740790","https://openalex.org/W7097413562","https://openalex.org/W4409916670","https://openalex.org/W2493574603","https://openalex.org/W2912047518","https://openalex.org/W4387104597"],"abstract_inverted_index":{"Two":[0],"combinatorial":[1],"rules":[2,89],"are":[3,90],"known":[4],"for":[5,153],"the":[6,26,34,43,58,64,70,79,82,87,96,107,119,131],"Grassmannian":[7],"Grothendieck":[8],"polynomial":[9],"$G^{(\u03b2)}_\u03bb$:":[10],"a":[11,23,30,76,128,145,150],"sum":[12,24],"over":[13,25],"set-valued":[14],"tableaux":[15],"of":[16,29,33,72,75,81,109,143],"shape":[17],"$\u03bb$,":[18],"due":[19,38],"to":[20,39,78,105,118],"Buch,":[21],"and":[22,42,121],"efficient":[27],"cells":[28,102,120,132,142],"cellular":[31],"decomposition":[32],"Gelfand-Zetlin":[35],"polytope":[36],"$GZ(\u03bb)$,":[37],"E.":[40],"Presnova":[41],"author.":[44],"All":[45],"coefficients":[46],"in":[47,85],"both":[48],"sums":[49],"equal":[50],"$1$.":[51],"We":[52,111],"construct":[53],"an":[54],"explicit":[55],"bijection":[56],"between":[57,134],"two":[59,88,135],"indexing":[60],"sets":[61],"which":[62],"matches":[63],"summands":[65],"term":[66],"by":[67],"term,":[68],"carrying":[69],"number":[71],"excess":[73],"entries":[74],"tableau":[77],"dimension":[80],"corresponding":[83],"cell;":[84],"particular":[86],"equivalent,":[91],"either":[92],"being":[93],"deducible":[94],"from":[95],"other.":[97],"The":[98],"efficiency":[99],"condition":[100],"on":[101],"turns":[103],"out":[104],"be":[106],"column-strictness":[108],"tableaux.":[110],"then":[112],"transport":[113],"Yu's":[114],"square-root":[115],"crystal":[116],"operators":[117],"find":[122],"that":[123],"they":[124],"respect":[125],"dimension,":[126],"along":[127],"double":[129],"$i$-string":[130],"alternate":[133],"consecutive":[136,141],"dimensions,":[137],"but":[138],"not":[139,148],"incidence:":[140],"such":[144],"string":[146],"need":[147],"share":[149],"point,":[151],"already":[152],"$\u03bb=(2,1,0)$.":[154]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-10T00:00:00"}
