{"id":"https://openalex.org/W3001604198","doi":"https://doi.org/10.1137/20m1320730","title":"Counting Linear Extensions of Posets with Determinants of Hook Lengths","display_name":"Counting Linear Extensions of Posets with Determinants of Hook Lengths","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3001604198","doi":"https://doi.org/10.1137/20m1320730","mag":"3001604198"},"language":"en","primary_location":{"id":"doi:10.1137/20m1320730","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1320730","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2001.08822","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072709242","display_name":"Alexander Garver","orcid":"https://orcid.org/0000-0002-0055-0956"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alexander Garver","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110685105","display_name":"Stefan N. Gr\u00f6sser","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stefan Grosser","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045577929","display_name":"Jacob P. Matherne","orcid":"https://orcid.org/0000-0002-6187-9771"},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"nonprofit","lineage":["https://openalex.org/I149899117"]},{"id":"https://openalex.org/I4210119712","display_name":"Max Planck Institute for Mathematics","ror":"https://ror.org/02dh8ja68","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210119712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jacob P. Matherne","raw_affiliation_strings":["Max Planck Institute for Mathematics, Max Planck Society"],"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Mathematics, Max Planck Society","institution_ids":["https://openalex.org/I4210119712","https://openalex.org/I149899117"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089720550","display_name":"Alejandro H. Morales","orcid":"https://orcid.org/0000-0002-2848-3230"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alejandro Morales","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5072709242"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6462,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.55995168,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"35","issue":"1","first_page":"205","last_page":"233"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9887999892234802,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9882000088691711,"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/mathematics","display_name":"Mathematics","score":0.7459185123443604},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7238666415214539},{"id":"https://openalex.org/keywords/skew","display_name":"Skew","score":0.6576327085494995},{"id":"https://openalex.org/keywords/hook","display_name":"Hook","score":0.6170883774757385},{"id":"https://openalex.org/keywords/ribbon","display_name":"Ribbon","score":0.5499222278594971},{"id":"https://openalex.org/keywords/star-product","display_name":"Star product","score":0.5129470229148865},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.44279319047927856},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.41961801052093506},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3580209016799927},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1105148196220398},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08698108792304993},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06427082419395447}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7459185123443604},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7238666415214539},{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.6576327085494995},{"id":"https://openalex.org/C2777586403","wikidata":"https://www.wikidata.org/wiki/Q4243098","display_name":"Hook","level":2,"score":0.6170883774757385},{"id":"https://openalex.org/C2780392137","wikidata":"https://www.wikidata.org/wiki/Q17121801","display_name":"Ribbon","level":2,"score":0.5499222278594971},{"id":"https://openalex.org/C195800304","wikidata":"https://www.wikidata.org/wiki/Q7601281","display_name":"Star product","level":2,"score":0.5129470229148865},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.44279319047927856},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.41961801052093506},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3580209016799927},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1105148196220398},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08698108792304993},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06427082419395447},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m1320730","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1320730","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2001.08822","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2001.08822","pdf_url":"https://arxiv.org/pdf/2001.08822","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"text"},{"id":"mag:3001604198","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2001.08822.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2001.08822","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2001.08822","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2001.08822","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2001.08822","pdf_url":"https://arxiv.org/pdf/2001.08822","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2165548363","display_name":null,"funder_award_id":"Canada","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G3433040227","display_name":"Combinatorics of Skew Tableaux and Flow Polytopes","funder_award_id":"1855536","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4980692079","display_name":null,"funder_award_id":"05999-2014","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G5784215521","display_name":null,"funder_award_id":"Chair","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G607235433","display_name":null,"funder_award_id":"1638352","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6221715925","display_name":null,"funder_award_id":"RGPIN","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G6868708400","display_name":null,"funder_award_id":"DMS-1638352","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8335196614","display_name":null,"funder_award_id":"RGPIN/","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8536456240","display_name":null,"funder_award_id":"RGPIN/05999-2014","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G8595721295","display_name":null,"funder_award_id":"NSERC","funder_id":"https://openalex.org/F4320320994","funder_display_name":"Canada Research Chairs"},{"id":"https://openalex.org/G8947572336","display_name":null,"funder_award_id":"DMS-1855536","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G919846122","display_name":null,"funder_award_id":"Chair","funder_id":"https://openalex.org/F4320320994","funder_display_name":"Canada Research Chairs"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320994","display_name":"Canada Research Chairs","ror":"https://ror.org/0517h6h17"},{"id":"https://openalex.org/F4320327553","display_name":"International Max Planck Research School for Advanced Methods in Process and Systems Engineering","ror":null},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3001604198.pdf","grobid_xml":"https://content.openalex.org/works/W3001604198.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W371866709","https://openalex.org/W1585310225","https://openalex.org/W1974745849","https://openalex.org/W1987721903","https://openalex.org/W1996959888","https://openalex.org/W1999545043","https://openalex.org/W2052049441","https://openalex.org/W2058773342","https://openalex.org/W2060478591","https://openalex.org/W2061219385","https://openalex.org/W2080139830","https://openalex.org/W2314376244","https://openalex.org/W2492707486","https://openalex.org/W2536100367","https://openalex.org/W2787956490","https://openalex.org/W2914659449","https://openalex.org/W2918018314","https://openalex.org/W2963742421","https://openalex.org/W2963791287","https://openalex.org/W2964036782","https://openalex.org/W2964087901","https://openalex.org/W2982570320","https://openalex.org/W2999009785","https://openalex.org/W3198160809","https://openalex.org/W4205448029"],"related_works":["https://openalex.org/W3132381913","https://openalex.org/W3154858542","https://openalex.org/W2066957577","https://openalex.org/W3007906716","https://openalex.org/W2786870567","https://openalex.org/W2950849601","https://openalex.org/W2974759044","https://openalex.org/W2536100367","https://openalex.org/W2281676492","https://openalex.org/W3038657745","https://openalex.org/W3034876490","https://openalex.org/W2004076922","https://openalex.org/W2061219385","https://openalex.org/W3006502557","https://openalex.org/W2474757319","https://openalex.org/W2000502447","https://openalex.org/W3124299311","https://openalex.org/W2952331631","https://openalex.org/W2117509168","https://openalex.org/W2076974687"],"abstract_inverted_index":{"We":[0,38],"introduce":[1],"a":[2,26,29],"class":[3],"of":[4,20,28,35,42,48,60,65,72,85,88,100],"posets,":[5,15,91],"which":[6],"includes":[7],"both":[8],"ribbon":[9],"posets":[10,62],"(skew":[11],"shapes)":[12],"and":[13,52,92,108],"$d$-complete":[14,90],"such":[16],"that":[17],"their":[18],"number":[19,84],"linear":[21,66,86],"extensions":[22,67,87],"is":[23],"given":[24,69],"by":[25,70,103],"determinant":[27],"matrix":[30],"whose":[31,63],"entries":[32],"are":[33,68],"products":[34],"hook":[36],"lengths.":[37],"also":[39],"give":[40,58,94],"$q$-analogues":[41],"this":[43],"determinantal":[44],"formula":[45],"in":[46],"terms":[47],"the":[49,83],"major":[50],"index":[51],"inversion":[53],"statistics.":[54],"As":[55],"applications,":[56],"we":[57,75,93],"families":[59],"tree":[61],"numbers":[64],"generalizations":[71],"Euler":[73],"numbers,":[74],"draw":[76],"relations":[77],"to":[78,98],"Naruse-Okada's":[79],"positive":[80],"formulas":[81],"for":[82],"skew":[89],"polynomiality":[95],"results":[96],"analogous":[97],"those":[99],"descent":[101],"polynomials":[102],"Diaz-L\u00f3pez,":[104],"Harris,":[105],"Insko,":[106],"Omar,":[107],"Sagan.":[109]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}