{"id":"https://openalex.org/W7127135429","doi":"https://doi.org/10.5070/c65465680","title":"Ryser's Theorem for symmetric \\(\\rho\\)-latin squares","display_name":"Ryser's Theorem for symmetric \\(\\rho\\)-latin squares","publication_year":2026,"publication_date":"2026-02-02","ids":{"openalex":"https://openalex.org/W7127135429","doi":"https://doi.org/10.5070/c65465680"},"language":null,"primary_location":{"id":"doi:10.5070/c65465680","is_oa":true,"landing_page_url":"https://doi.org/10.5070/c65465680","pdf_url":"https://escholarship.org/content/qt9358h7wf/qt9358h7wf.pdf","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://escholarship.org/content/qt9358h7wf/qt9358h7wf.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120281626","display_name":"Amin Bahmanian","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Amin Bahmanian","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5124757386","display_name":"A. J. W. Hilton","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. J. W. Hilton","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5120281626"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.40776537,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"5","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9611999988555908,"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":0.9611999988555908,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.014800000004470348,"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/T10849","display_name":"Finite Group Theory Research","score":0.0031999999191612005,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.582099974155426},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5587999820709229},{"id":"https://openalex.org/keywords/symbol","display_name":"Symbol (formal)","score":0.5561000108718872},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.4927999973297119},{"id":"https://openalex.org/keywords/legendre-symbol","display_name":"Legendre symbol","score":0.3562000095844269}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8296999931335449},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.582099974155426},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5587999820709229},{"id":"https://openalex.org/C134400042","wikidata":"https://www.wikidata.org/wiki/Q2372244","display_name":"Symbol (formal)","level":2,"score":0.5561000108718872},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4934999942779541},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.4927999973297119},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40880000591278076},{"id":"https://openalex.org/C165656649","wikidata":"https://www.wikidata.org/wiki/Q748339","display_name":"Legendre symbol","level":5,"score":0.3562000095844269},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.3019999861717224},{"id":"https://openalex.org/C158887663","wikidata":"https://www.wikidata.org/wiki/Q679367","display_name":"Latin square","level":4,"score":0.29589998722076416},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26019999384880066}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5070/c65465680","is_oa":true,"landing_page_url":"https://doi.org/10.5070/c65465680","pdf_url":"https://escholarship.org/content/qt9358h7wf/qt9358h7wf.pdf","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},{"id":"pmh:doi:10.5070/C65465680","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S7407050878","display_name":"California Digital Library","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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/journal article"}],"best_oa_location":{"id":"doi:10.5070/c65465680","is_oa":true,"landing_page_url":"https://doi.org/10.5070/c65465680","pdf_url":"https://escholarship.org/content/qt9358h7wf/qt9358h7wf.pdf","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7127135429.pdf","grobid_xml":"https://content.openalex.org/works/W7127135429.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Let":[0],"\\(L\\)":[1,46,68],"be":[2,48,154],"an":[3,161],"\\(n\\times":[4],"n\\)":[5,123],"array":[6],"whose":[7],"top":[8,118],"left":[9,119],"\\(r\\times":[10,122],"r\\)":[11],"subarray":[12,120],"is":[13,69,99,121,127],"filled":[14,49],"with":[15,71],"\\(k\\)":[16],"different":[17],"symbols,":[18],"each":[19,25,32,52,59,66,78,96],"occurring":[20],"at":[21,28,55,62],"most":[22,29,56,63],"once":[23,30,57,64],"in":[24,31,58,65,86],"row":[26,60],"and":[27,37,61,77,113,124],"column.":[33],"We":[34],"establish":[35],"necessary":[36],"sufficient":[38],"conditions":[39],"that":[40,51],"ensure":[41],"the":[42,74,91,114,117,125,147,150,164],"remaining":[43],"cells":[44],"of":[45,84,94,149,163,168],"can":[47],"such":[50],"symbol":[53,79,97],"occurs":[54,80,98],"column,":[67],"symmetric":[70],"respect":[72],"to":[73,153,160],"main":[75,151],"diagonal,":[76],"a":[81],"prescribed":[82,92],"number":[83,93],"times":[85,95],"\\(L\\).":[87],"The":[88],"case":[89,115],"where":[90,116],"\\(n\\)":[100],"was":[101,130],"solved":[102],"by":[103,132],"Cruse":[104],"(J.":[105,136],"Combin.":[106,137,176],"Theory":[107,138],"Ser.":[108,139],"A":[109,140],"16":[110],"(1974),":[111],"18-22),":[112],"symmetry":[126],"not":[128],"required,":[129],"settled":[131],"Goldwasser":[133],"et":[134],"al.":[135],"130":[141],"(2015),":[142],"26-41).":[143],"Our":[144],"result":[145],"allows":[146],"entries":[148],"diagonal":[152],"specified":[155],"as":[156],"well,":[157],"which":[158],"leads":[159],"extension":[162],"Andersen-Hoffman":[165],"Theorem":[166],"(Annals":[167],"Disc.":[169],"Math.":[170],"15":[171],"(1982)":[172],"9-26,":[173],"European":[174],"J.":[175],"4":[177],"(1983)":[178],"33-35).Mathematics":[179],"Subject":[180],"Classifications:":[181],"05B15,":[182],"05C70,":[183],"05C15Keywords:":[184],"Latin":[185],"square,":[186],"embedding,":[187],"\\((g,f)\\)-factors,":[188],"Cruse's":[189],"Theorem,":[190,192,194],"Andersen-Hoffman's":[191],"Ryser's":[193],"amalgamation,":[195],"detachment":[196]},"counts_by_year":[],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2026-02-03T00:00:00"}