{"id":"https://openalex.org/W2301785981","doi":"https://doi.org/10.37236/5237","title":"New Duality Operator for Complex Circulant Matrices and a Conjecture of Ryser","display_name":"New Duality Operator for Complex Circulant Matrices and a Conjecture of Ryser","publication_year":2016,"publication_date":"2016-03-18","ids":{"openalex":"https://openalex.org/W2301785981","doi":"https://doi.org/10.37236/5237","mag":"2301785981"},"language":"en","primary_location":{"id":"doi:10.37236/5237","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5237","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p59/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p59/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111512566","display_name":"Luis H. Gallardo","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Luis H. Gallardo","raw_affiliation_strings":["University of Brest"],"affiliations":[{"raw_affiliation_string":"University of Brest","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5111512566"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1838,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.54752983,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"23","issue":"1","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":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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9957000017166138,"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"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.8808338642120361},{"id":"https://openalex.org/keywords/circulant-matrix","display_name":"Circulant matrix","score":0.7620357275009155},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7262995839118958},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.639879584312439},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5683732032775879},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5589103698730469},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.5373543500900269},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5345308780670166},{"id":"https://openalex.org/keywords/hadamard-matrix","display_name":"Hadamard matrix","score":0.5228043794631958},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5057802200317383},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.4307059049606323},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.41609951853752136},{"id":"https://openalex.org/keywords/complex-hadamard-matrix","display_name":"Complex Hadamard matrix","score":0.4142257571220398},{"id":"https://openalex.org/keywords/hadamards-maximal-determinant-problem","display_name":"Hadamard's maximal determinant problem","score":0.41362008452415466},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38737478852272034},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30390143394470215},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08707752823829651}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8808338642120361},{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.7620357275009155},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7262995839118958},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.639879584312439},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5683732032775879},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5589103698730469},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.5373543500900269},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5345308780670166},{"id":"https://openalex.org/C30463267","wikidata":"https://www.wikidata.org/wiki/Q1422682","display_name":"Hadamard matrix","level":3,"score":0.5228043794631958},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5057802200317383},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.4307059049606323},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.41609951853752136},{"id":"https://openalex.org/C6497535","wikidata":"https://www.wikidata.org/wiki/Q5156556","display_name":"Complex Hadamard matrix","level":4,"score":0.4142257571220398},{"id":"https://openalex.org/C121334634","wikidata":"https://www.wikidata.org/wiki/Q5637579","display_name":"Hadamard's maximal determinant problem","level":5,"score":0.41362008452415466},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38737478852272034},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30390143394470215},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08707752823829651},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/5237","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5237","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p59/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/5237","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5237","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p59/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.5299999713897705}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2301785981.pdf","grobid_xml":"https://content.openalex.org/works/W2301785981.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W401986301","https://openalex.org/W1523337958","https://openalex.org/W1601213298","https://openalex.org/W1957100706","https://openalex.org/W1971847304","https://openalex.org/W2029700997","https://openalex.org/W2040687693","https://openalex.org/W2065609889","https://openalex.org/W2093711931","https://openalex.org/W2097099020","https://openalex.org/W2186972632","https://openalex.org/W2321280303","https://openalex.org/W2340561673","https://openalex.org/W3102541665","https://openalex.org/W4238816768","https://openalex.org/W4300455938","https://openalex.org/W6632654815","https://openalex.org/W6704368321","https://openalex.org/W6785398099"],"related_works":["https://openalex.org/W1976224891","https://openalex.org/W1971692815","https://openalex.org/W4226106482","https://openalex.org/W2796326658","https://openalex.org/W4313302755","https://openalex.org/W2003940980","https://openalex.org/W2131599704","https://openalex.org/W2054788067","https://openalex.org/W2740594951","https://openalex.org/W2010617738"],"abstract_inverted_index":{"We":[0,51],"associate":[1],"to":[2],"any":[3],"given":[4],"circulant":[5,23,64],"complex":[6],"matrix":[7],"$C$":[8],"another":[9],"one":[10],"$E(C)$":[11],"such":[12],"that":[13,56,61,72,77,83],"$E(E(C))":[14],"=":[15],"C^{*}$":[16],"the":[17,37,41,62,79,92,103],"transpose":[18],"conjugate":[19],"of":[20,26,40,43,67,85,88,95,98,100],"$C.$":[21],"All":[22],"Hadamard":[24,65],"matrices":[25,66],"order":[27,68],"$4$":[28],"satisfy":[29,73],"a":[30,54,74,86],"condition":[31,75,80],"$C_4$":[32,81],"on":[33],"their":[34],"eigenvalues,":[35],"namely,":[36],"absolute":[38,93],"value":[39,94],"sum":[42],"all":[44],"eigenvalues":[45,99],"is":[46],"bounded":[47],"above":[48],"by":[49,53],"$2.$":[50],"prove":[52],"\"descent\"":[55],"uses":[57],"our":[58],"operator":[59],"$E$":[60],"only":[63],"$n":[69],"\\geq":[70],"4$,":[71],"$C_n$":[76],"generalizes":[78],"and":[82],"consist":[84],"list":[87],"$n/4$":[89],"inequalities":[90],"for":[91],"some":[96],"sums":[97],"$H$":[101],"are":[102],"known":[104],"ones.":[105]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}