{"id":"https://openalex.org/W2006129849","doi":"https://doi.org/10.1137/090773751","title":"The Conjectures of Alon\u2013Tarsi and Rota in Dimension Prime Minus One","display_name":"The Conjectures of Alon\u2013Tarsi and Rota in Dimension Prime Minus One","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2006129849","doi":"https://doi.org/10.1137/090773751","mag":"2006129849"},"language":"en","primary_location":{"id":"doi:10.1137/090773751","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090773751","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":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071001252","display_name":"David G. Glynn","orcid":"https://orcid.org/0000-0002-6399-7771"},"institutions":[{"id":"https://openalex.org/I169541294","display_name":"Flinders University","ror":"https://ror.org/01kpzv902","country_code":"AU","type":"education","lineage":["https://openalex.org/I169541294"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"David G. Glynn","raw_affiliation_strings":["davidg@csem.flinders.edu.au and david.glynn@csem.flinders.edu.au and dglynn@me.com#TAB#"],"affiliations":[{"raw_affiliation_string":"davidg@csem.flinders.edu.au and david.glynn@csem.flinders.edu.au and dglynn@me.com#TAB#","institution_ids":["https://openalex.org/I169541294"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5071001252"],"corresponding_institution_ids":["https://openalex.org/I169541294"],"apc_list":null,"apc_paid":null,"fwci":3.821,"has_fulltext":false,"cited_by_count":52,"citation_normalized_percentile":{"value":0.93381022,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"24","issue":"2","first_page":"394","last_page":"399"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9958000183105469,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.995199978351593,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8905473947525024},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7923063039779663},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6536540985107422},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6061704158782959},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.5909117460250854},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5632071495056152},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5173363089561462},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4838317930698395},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.4740580916404724},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.455890953540802},{"id":"https://openalex.org/keywords/latin-square","display_name":"Latin square","score":0.4388406276702881},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.428778737783432},{"id":"https://openalex.org/keywords/prime-number","display_name":"Prime number","score":0.4149984121322632},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.4105824828147888},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3695957064628601},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15636399388313293},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08128935098648071}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8905473947525024},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7923063039779663},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6536540985107422},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6061704158782959},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.5909117460250854},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5632071495056152},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5173363089561462},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4838317930698395},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4740580916404724},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.455890953540802},{"id":"https://openalex.org/C158887663","wikidata":"https://www.wikidata.org/wiki/Q679367","display_name":"Latin square","level":4,"score":0.4388406276702881},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.428778737783432},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.4149984121322632},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.4105824828147888},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3695957064628601},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15636399388313293},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08128935098648071},{"id":"https://openalex.org/C70262065","wikidata":"https://www.wikidata.org/wiki/Q427652","display_name":"Rumen","level":3,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C31903555","wikidata":"https://www.wikidata.org/wiki/Q1637030","display_name":"Food science","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C100544194","wikidata":"https://www.wikidata.org/wiki/Q41760","display_name":"Fermentation","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/090773751","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090773751","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:dspace.flinders.edu.au:2328/31404","is_oa":false,"landing_page_url":"http://hdl.handle.net/2328/31404","pdf_url":null,"source":{"id":"https://openalex.org/S4306401119","display_name":"Flinders Academic Commons (Flinders University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169541294","host_organization_name":"Flinders University","host_organization_lineage":["https://openalex.org/I169541294"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1520990686","https://openalex.org/W1558934860","https://openalex.org/W1954214817","https://openalex.org/W1983222127","https://openalex.org/W1988918747","https://openalex.org/W1992906119","https://openalex.org/W2024761979","https://openalex.org/W2033554236","https://openalex.org/W2039481874","https://openalex.org/W2052688974","https://openalex.org/W2063117789","https://openalex.org/W2072414205","https://openalex.org/W2082199499","https://openalex.org/W2094412891","https://openalex.org/W2158254279","https://openalex.org/W2325582968","https://openalex.org/W2490010345","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2393403800","https://openalex.org/W2326647168","https://openalex.org/W1990217685","https://openalex.org/W2412284786","https://openalex.org/W928614972","https://openalex.org/W2092976320","https://openalex.org/W2010060099","https://openalex.org/W4206835815","https://openalex.org/W2057368420","https://openalex.org/W2009214945"],"abstract_inverted_index":{"A":[0],"formula":[1],"for":[2,81,160],"Glynn's":[3],"hyperdeterminant":[4],"$\\det_p$":[5],"(p":[6],"prime)":[7],"of":[8,16,41,55,59,68,72,85,91,127,136,145,163],"a":[9,82,102,112,115,167],"square":[10],"matrix":[11,24],"shows":[12],"that":[13,52,73,118,130,133],"the":[14,39,53,66,122,134,143,152],"number":[15,40,54,67,135,144],"ways":[17,42],"to":[18,65,120],"decompose":[19],"any":[20,89],"integral":[21],"doubly":[22],"stochastic":[23],"with":[25,35,43],"row":[26],"and":[27,96,129],"column":[28],"sums":[29],"$p-1$":[30,32,61,87],"into":[31],"permutation":[33],"matrices":[34],"even":[36,56,137,164],"product,":[37,45],"minus":[38],"odd":[44,69,146],"is":[46,62,79,106,111,140,151,169],"1":[47],"(mod":[48],"p).":[49],"It":[50,105],"follows":[51],"Latin":[57,70,138,147],"squares":[58,71,139],"order":[60],"not":[63],"equal":[64],"order.":[74],"Thus":[75],"Rota's":[76,157],"basis":[77,158],"conjecture":[78,159],"true":[80],"vector":[83,161],"space":[84],"dimension":[86,165],"over":[88,166],"field":[90,168],"characteristic":[92],"zero":[93],"or":[94],"p,":[95],"all":[97],"other":[98],"characteristics":[99],"except":[100],"possibly":[101],"finite":[103],"number.":[104],"also":[107,131],"shown":[108],"where":[109,156],"there":[110],"mistake":[113],"in":[114],"published":[116],"proof":[117],"claimed":[119,132],"multiply":[121],"known":[123],"dimensions":[124],"by":[125],"powers":[126],"two,":[128],"greater":[141],"than":[142],"squares.":[148],"Now,":[149],"26":[150],"smallest":[153],"unknown":[154],"case":[155],"spaces":[162],"unsolved.":[170]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":8}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
