{"id":"https://openalex.org/W1834517917","doi":"https://doi.org/10.37236/267","title":"Cayley Graphs on the Symmetric Group Generated by Initial Reversals have Unit Spectral Gap","display_name":"Cayley Graphs on the Symmetric Group Generated by Initial Reversals have Unit Spectral Gap","publication_year":2009,"publication_date":"2009-10-12","ids":{"openalex":"https://openalex.org/W1834517917","doi":"https://doi.org/10.37236/267","mag":"1834517917"},"language":"en","primary_location":{"id":"doi:10.37236/267","is_oa":true,"landing_page_url":"https://doi.org/10.37236/267","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1n29/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":null,"license_id":null,"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/v16i1n29/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037938838","display_name":"Filippo Cesi","orcid":"https://orcid.org/0000-0001-7188-2010"},"institutions":[{"id":"https://openalex.org/I4210109836","display_name":"Instituto de F\u00edsica La Plata","ror":"https://ror.org/01pmtm379","country_code":"AR","type":"facility","lineage":["https://openalex.org/I151201029","https://openalex.org/I4210109836","https://openalex.org/I4210123736","https://openalex.org/I4210138160","https://openalex.org/I4387155568","https://openalex.org/I874386039"]}],"countries":["AR"],"is_corresponding":true,"raw_author_name":"Filippo Cesi","raw_affiliation_strings":["FISICA"],"affiliations":[{"raw_affiliation_string":"FISICA","institution_ids":["https://openalex.org/I4210109836"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5037938838"],"corresponding_institution_ids":["https://openalex.org/I4210109836"],"apc_list":null,"apc_paid":null,"fwci":0.8646,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.74215892,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"16","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.996999979019165,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.996999979019165,"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/T11476","display_name":"Graph theory and applications","score":0.9915000200271606,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9909999966621399,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8446581959724426},{"id":"https://openalex.org/keywords/cayley-graph","display_name":"Cayley graph","score":0.8026832342147827},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7143821120262146},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"Symmetric group","score":0.5894438028335571},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5625149607658386},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.48927542567253113},{"id":"https://openalex.org/keywords/spectral-gap","display_name":"Spectral gap","score":0.4715053141117096},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.4689224362373352},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.4668809771537781},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4640815258026123},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.4565138816833496},{"id":"https://openalex.org/keywords/cayley-transform","display_name":"Cayley transform","score":0.4428630769252777},{"id":"https://openalex.org/keywords/assertion","display_name":"Assertion","score":0.4225006699562073},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3259769678115845},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.1508254110813141},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.10957816243171692},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06710413098335266}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8446581959724426},{"id":"https://openalex.org/C120204988","wikidata":"https://www.wikidata.org/wiki/Q859174","display_name":"Cayley graph","level":3,"score":0.8026832342147827},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7143821120262146},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.5894438028335571},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5625149607658386},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.48927542567253113},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.4715053141117096},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.4689224362373352},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.4668809771537781},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4640815258026123},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.4565138816833496},{"id":"https://openalex.org/C18586221","wikidata":"https://www.wikidata.org/wiki/Q2778065","display_name":"Cayley transform","level":5,"score":0.4428630769252777},{"id":"https://openalex.org/C40422974","wikidata":"https://www.wikidata.org/wiki/Q741248","display_name":"Assertion","level":2,"score":0.4225006699562073},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3259769678115845},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.1508254110813141},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.10957816243171692},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06710413098335266},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer 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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/267","is_oa":true,"landing_page_url":"https://doi.org/10.37236/267","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1n29/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.214.3614","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.214.3614","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_16/PDF/v16i1n29.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.313.4321","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.313.4321","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0904.1800v1.pdf","raw_type":"text"},{"id":"pmh:oai:iris.uniroma1.it:11573/66648","is_oa":false,"landing_page_url":"http://www.scopus.com/inward/record.url?eid=2-s2.0-70350176787&partnerID=65&md5=b8f79b89abcde98b3dfe419cd4dfb611","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"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":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.37236/267","is_oa":true,"landing_page_url":"https://doi.org/10.37236/267","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1n29/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1834517917.pdf","grobid_xml":"https://content.openalex.org/works/W1834517917.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W141723088","https://openalex.org/W1518468345","https://openalex.org/W1600293573","https://openalex.org/W1874018431","https://openalex.org/W1969083090","https://openalex.org/W2015569722","https://openalex.org/W2022507394","https://openalex.org/W2046944251","https://openalex.org/W2056389572","https://openalex.org/W2068112586","https://openalex.org/W2068785829","https://openalex.org/W2069626659","https://openalex.org/W2069866079","https://openalex.org/W2156024151","https://openalex.org/W2318438148","https://openalex.org/W2967948787"],"related_works":["https://openalex.org/W4293876796","https://openalex.org/W2298820818","https://openalex.org/W1832592836","https://openalex.org/W2096663817","https://openalex.org/W2897328500","https://openalex.org/W3132233781","https://openalex.org/W2886702391","https://openalex.org/W4298090406","https://openalex.org/W2952661156","https://openalex.org/W1834517917"],"abstract_inverted_index":{"In":[0,33],"a":[1,68,86],"recent":[2],"paper":[3],"Gunnells,":[4],"Scott":[5],"and":[6,28,51],"Walden":[7],"have":[8],"determined":[9],"the":[10,14,18,23,38,46,62,77,80,94],"complete":[11],"spectrum":[12],"of":[13,45,71,79,82,89,93],"Schreier":[15],"graph":[16],"on":[17,76],"symmetric":[19,95],"group":[20],"corresponding":[21,63],"to":[22],"Young":[24],"subgroup":[25],"$S_{n-2}\\times":[26],"S_2$":[27],"generated":[29],"by":[30],"initial":[31],"reversals.":[32],"particular":[34],"they":[35],"find":[36],"that":[37,53,57],"first":[39],"nonzero":[40],"eigenvalue,":[41],"or":[42],"spectral":[43],"gap,":[44],"Laplacian":[47,81],"is":[48],"always":[49],"1,":[50],"report":[52],"\"empirical":[54],"evidence\"":[55],"suggests":[56],"this":[58,72],"also":[59],"holds":[60],"for":[61],"Cayley":[64,83],"graph.":[65],"We":[66],"provide":[67],"simple":[69],"proof":[70],"last":[73],"assertion,":[74],"based":[75],"decomposition":[78],"graphs,":[84],"into":[85],"direct":[87],"sum":[88],"irreducible":[90],"representation":[91],"matrices":[92],"group.":[96]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2015,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
