{"id":"https://openalex.org/W2161533967","doi":"https://doi.org/10.1090/s0025-5718-98-00964-8","title":"The efficient computation of Fourier transforms on the symmetric group","display_name":"The efficient computation of Fourier transforms on the symmetric group","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2161533967","doi":"https://doi.org/10.1090/s0025-5718-98-00964-8","mag":"2161533967"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-98-00964-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00964-8","pdf_url":"https://www.ams.org/mcom/1998-67-223/S0025-5718-98-00964-8/S0025-5718-98-00964-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/1998-67-223/S0025-5718-98-00964-8/S0025-5718-98-00964-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027308610","display_name":"David K. Maslen","orcid":null},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832","https://openalex.org/I4405262988"]},{"id":"https://openalex.org/I84909340","display_name":"Institut des Hautes \u00c9tudes Scientifiques","ror":"https://ror.org/05d5m2r55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I84909340"]}],"countries":["FR","NL"],"is_corresponding":true,"raw_author_name":"David Maslen","raw_affiliation_strings":["Centrum voor Wiskunde en Informatica, Kruislaan 413, 1098SJ, Amsterdam, The Netherlands","Institut des Haute \u00c3\u0089tudes Scientifiques, Le Bois-Marie, 35 Route de Chartres, 91440, Bures-sur-Yvette, France","Institut des Haute \u00c9tudes Scientifiques, Le Bois-Marie, 35 Route de Chartres, 91440, Bures-sur-Yvette, France"],"affiliations":[{"raw_affiliation_string":"Centrum voor Wiskunde en Informatica, Kruislaan 413, 1098SJ, Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I1341640284"]},{"raw_affiliation_string":"Institut des Haute \u00c3\u0089tudes Scientifiques, Le Bois-Marie, 35 Route de Chartres, 91440, Bures-sur-Yvette, France","institution_ids":["https://openalex.org/I84909340"]},{"raw_affiliation_string":"Institut des Haute \u00c9tudes Scientifiques, Le Bois-Marie, 35 Route de Chartres, 91440, Bures-sur-Yvette, France","institution_ids":["https://openalex.org/I84909340"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5027308610"],"corresponding_institution_ids":["https://openalex.org/I1341640284","https://openalex.org/I84909340"],"apc_list":null,"apc_paid":null,"fwci":0.5533,"has_fulltext":true,"cited_by_count":48,"citation_normalized_percentile":{"value":0.66704018,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"67","issue":"223","first_page":"1121","last_page":"1147"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9997000098228455,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9991000294685364,"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/algorithm","display_name":"Algorithm","score":0.6958527565002441},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41249018907546997},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3999299705028534}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6958527565002441},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41249018907546997},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3999299705028534}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1090/s0025-5718-98-00964-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00964-8","pdf_url":"https://www.ams.org/mcom/1998-67-223/S0025-5718-98-00964-8/S0025-5718-98-00964-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.192.1631","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.1631","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/journals/mcom/1998-67-223/S0025-5718-98-00964-8/S0025-5718-98-00964-8.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.36.802","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.36.802","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.dartmouth.edu/~maslen/sym-t.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.97.459","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.97.459","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/1998-67-223/S0025-5718-98-00964-8/S0025-5718-98-00964-8.pdf","raw_type":"text"},{"id":"pmh:oai:cds.cern.ch:311051","is_oa":false,"landing_page_url":"http://cds.cern.ch/record/311051","pdf_url":null,"source":{"id":"https://openalex.org/S4306402195","display_name":"CERN Document Server (European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-98-00964-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00964-8","pdf_url":"https://www.ams.org/mcom/1998-67-223/S0025-5718-98-00964-8/S0025-5718-98-00964-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321010","display_name":"Universiteit Utrecht","ror":"https://ror.org/04pp8hn57"},{"id":"https://openalex.org/F4320337227","display_name":"Institut des Hautes \u00c9tudes Scientifiques, Universit\u00e9 Paris-Saclay","ror":"https://ror.org/05d5m2r55"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2161533967.pdf","grobid_xml":"https://content.openalex.org/works/W2161533967.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W1500032036","https://openalex.org/W1500894486","https://openalex.org/W1503154552","https://openalex.org/W1551735658","https://openalex.org/W1561337879","https://openalex.org/W1566547745","https://openalex.org/W1596185498","https://openalex.org/W1596709027","https://openalex.org/W1971407031","https://openalex.org/W1986263670","https://openalex.org/W2026411617","https://openalex.org/W2046563944","https://openalex.org/W2061171222","https://openalex.org/W2068803999","https://openalex.org/W2073215417","https://openalex.org/W2089998550","https://openalex.org/W2134984950","https://openalex.org/W2327162874","https://openalex.org/W2330548796","https://openalex.org/W2401450608","https://openalex.org/W2403334562","https://openalex.org/W2735674197","https://openalex.org/W3022389176","https://openalex.org/W3148121670","https://openalex.org/W3159676034","https://openalex.org/W4231896027","https://openalex.org/W4253674326","https://openalex.org/W4253701928","https://openalex.org/W4256035145","https://openalex.org/W4302389414","https://openalex.org/W6793722147"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2317200988","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278"],"abstract_inverted_index":{"This":[0],"paper":[1],"introduces":[2],"new":[3],"techniques":[4],"for":[5,164],"the":[6,21,39,53,142],"efficient":[7],"computation":[8],"of":[9,56,145,148],"Fourier":[10,54],"transforms":[11,166,168],"on":[12,59,169],"symmetric":[13],"groups":[14],"and":[15,37,141,167],"their":[16],"homogeneous":[17,170],"spaces.":[18,171],"We":[19,160],"replace":[20],"matrix":[22],"multiplications":[23,140],"in":[24,41,78],"Clausen\u2019s":[25],"algorithm":[26,49,150],"with":[27],"sums":[28],"indexed":[29],"by":[30],"combinatorial":[31,154],"objects":[32],"that":[33,156],"generalize":[34,157],"Young":[35],"tableaux,":[36],"write":[38],"result":[40],"a":[42,57],"form":[43],"similar":[44],"to":[45,152],"Horner\u2019s":[46],"rule.":[47],"The":[48],"we":[50],"obtain":[51],"computes":[52],"transform":[55],"function":[58],"<inline-formula":[60,82],"content-type=\"math/mathml\">":[61,83],"<mml:math":[62,84],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[63,85],"alttext=\"upper":[64],"S":[65,96],"Subscript":[66,97],"n\">":[67],"<mml:semantics>":[68,101],"<mml:msub>":[69,122],"<mml:mi>S</mml:mi>":[70,123],"<mml:mi>n</mml:mi>":[71,107,110,124],"</mml:msub>":[72,125],"<mml:annotation":[73,132],"encoding=\"application/x-tex\">S_n</mml:annotation>":[74],"</mml:semantics>":[75,137],"</mml:math>":[76,138],"</inline-formula>":[77,139],"no":[79],"more":[80],"than":[81],"alttext=\"three":[86],"fourths":[87],"n":[88,90,98],"left-parenthesis":[89],"minus":[91],"1":[92],"right-parenthesis":[93],"StartAbsoluteValue":[94],"upper":[95],"Baseline":[99],"EndAbsoluteValue\">":[100],"<mml:mrow>":[102],"<mml:mfrac>":[103],"<mml:mn>3</mml:mn>":[104],"<mml:mn>4</mml:mn>":[105],"</mml:mfrac>":[106],"<mml:mo":[108,115,119,128],"stretchy=\"false\">(</mml:mo>":[109],"<mml:mo>":[111],"\u2212":[112],"</mml:mo>":[113],"<mml:mn>1</mml:mn>":[114],"stretchy=\"false\">)</mml:mo>":[116],"<mml:mrow":[117,126],"class=\"MJX-TeXAtom-ORD\">":[118,127],"stretchy=\"false\">|</mml:mo>":[120,129],"</mml:mrow>":[121,130,131],"encoding=\"application/x-tex\">\\frac":[133],"{3}{4}":[134],"n(n-1)":[135],"|S_n|</mml:annotation>":[136],"same":[143],"number":[144],"additions.":[146],"Analysis":[147],"our":[149],"leads":[151],"several":[153],"problems":[155],"path":[158],"counting.":[159],"prove":[161],"corresponding":[162],"results":[163],"inverse":[165]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}