{"id":"https://openalex.org/W3191609791","doi":"https://doi.org/10.1080/00029890.2022.2115803","title":"A Determinantal Identity for the Permanent of a Rank 2 Matrix","display_name":"A Determinantal Identity for the Permanent of a Rank 2 Matrix","publication_year":2022,"publication_date":"2022-09-26","ids":{"openalex":"https://openalex.org/W3191609791","doi":"https://doi.org/10.1080/00029890.2022.2115803","mag":"3191609791"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2022.2115803","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2022.2115803","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/297201","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035697843","display_name":"Adam W. Marcus","orcid":"https://orcid.org/0000-0002-3227-903X"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Adam W. Marcus","raw_affiliation_strings":["\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland"],"raw_orcid":"https://orcid.org/0000-0002-3227-903X","affiliations":[{"raw_affiliation_string":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5035697843"],"corresponding_institution_ids":["https://openalex.org/I5124864"],"apc_list":null,"apc_paid":null,"fwci":0.2466,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.53299066,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"129","issue":"10","first_page":"962","last_page":"971"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11716","display_name":"Random Matrices and Applications","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9986000061035156,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9980000257492065,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.7624273300170898},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.7492235898971558},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7152994871139526},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.565646231174469},{"id":"https://openalex.org/keywords/identity-matrix","display_name":"Identity matrix","score":0.5533386468887329},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5157449841499329},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5151315927505493},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4978053569793701},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.4958260953426361},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.4351252615451813},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2792091369628906},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.1404697597026825},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.1087830662727356},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0953143835067749},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.08313921093940735}],"concepts":[{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.7624273300170898},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.7492235898971558},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7152994871139526},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.565646231174469},{"id":"https://openalex.org/C134567657","wikidata":"https://www.wikidata.org/wiki/Q193794","display_name":"Identity matrix","level":3,"score":0.5533386468887329},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5157449841499329},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5151315927505493},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4978053569793701},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.4958260953426361},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.4351252615451813},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2792091369628906},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.1404697597026825},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.1087830662727356},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0953143835067749},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.08313921093940735},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"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/C107038049","wikidata":"https://www.wikidata.org/wiki/Q35986","display_name":"Aesthetics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00029890.2022.2115803","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2022.2115803","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},{"id":"pmh:oai:infoscience.epfl.ch:297201","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/297201","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"WoS","raw_type":"research article"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:297201","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/297201","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"WoS","raw_type":"research article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.550000011920929}],"awards":[{"id":"https://openalex.org/G3794900144","display_name":null,"funder_award_id":"DMS-1552520","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1969554525","https://openalex.org/W1985376214","https://openalex.org/W1995238279","https://openalex.org/W2245829837","https://openalex.org/W2317079780","https://openalex.org/W2776898720","https://openalex.org/W2904639156","https://openalex.org/W2927801616","https://openalex.org/W2964343554"],"related_works":["https://openalex.org/W2361403716","https://openalex.org/W2904061867","https://openalex.org/W4289115725","https://openalex.org/W3144644423","https://openalex.org/W2024384195","https://openalex.org/W2605759486","https://openalex.org/W2379646217","https://openalex.org/W2143620739","https://openalex.org/W2031629316","https://openalex.org/W2551884148"],"abstract_inverted_index":{"We":[0],"prove":[1],"an":[2,32,73],"identity":[3,33,51],"relating":[4],"the":[5,13,22,25,39,67],"permanent":[6],"of":[7,15,34,47,54,69,75,79],"a":[8,76],"rank":[9],"2":[10],"matrix":[11],"and":[12,36,58,81],"determinants":[14],"its":[16],"Hadamard":[17],"powers.":[18],"When":[19],"viewed":[20],"in":[21,83],"right":[23],"way,":[24],"resulting":[26],"formula":[27],"looks":[28],"strikingly":[29],"similar":[30],"to":[31],"Carlitz":[35],"Levine,":[37],"suggesting":[38],"possibility":[40],"that":[41],"these":[42],"are":[43],"actually":[44],"special":[45],"cases":[46],"some":[48,63],"more":[49],"general":[50],"(or":[52],"class":[53],"identities)":[55],"connecting":[56],"permanents":[57],"determinants.":[59],"The":[60],"proof":[61],"combines":[62],"basic":[64],"facts":[65],"from":[66],"theory":[68],"symmetric":[70],"functions":[71],"with":[72],"application":[74],"famous":[77],"theorem":[78],"Binet":[80],"Cauchy":[82],"linear":[84],"algebra.":[85]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
