{"id":"https://openalex.org/W1874018431","doi":"https://doi.org/10.37236/961","title":"On Certain Integral Schreier Graphs of the Symmetric Group","display_name":"On Certain Integral Schreier Graphs of the Symmetric Group","publication_year":2007,"publication_date":"2007-05-31","ids":{"openalex":"https://openalex.org/W1874018431","doi":"https://doi.org/10.37236/961","mag":"1874018431"},"language":"en","primary_location":{"id":"doi:10.37236/961","is_oa":true,"landing_page_url":"https://doi.org/10.37236/961","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1r43/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/v14i1r43/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016465722","display_name":"Paul E. Gunnells","orcid":"https://orcid.org/0000-0002-2742-3025"},"institutions":[{"id":"https://openalex.org/I16269868","display_name":"Santa Clara University","ror":"https://ror.org/03ypqe447","country_code":"US","type":"education","lineage":["https://openalex.org/I16269868"]},{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Paul E. Gunnells","raw_affiliation_strings":["Department of Mathematics and Computer Science Santa Clara University Santa Clara, California, USA","Department of Mathematics and Statistics","University of Massachusetts Amherst, Massachusetts, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science Santa Clara University Santa Clara, California, USA","institution_ids":["https://openalex.org/I16269868"]},{"raw_affiliation_string":"Department of Mathematics and Statistics","institution_ids":[]},{"raw_affiliation_string":"University of Massachusetts Amherst, Massachusetts, USA","institution_ids":["https://openalex.org/I24603500"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109530428","display_name":"Richard A. Scott","orcid":null},"institutions":[{"id":"https://openalex.org/I16269868","display_name":"Santa Clara University","ror":"https://ror.org/03ypqe447","country_code":"US","type":"education","lineage":["https://openalex.org/I16269868"]},{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard A. Scott","raw_affiliation_strings":["University of Massachusetts Amherst, Massachusetts, USA","Department of Mathematics and Statistics","Department of Mathematics and Computer Science Santa Clara University Santa Clara, California, USA"],"affiliations":[{"raw_affiliation_string":"University of Massachusetts Amherst, Massachusetts, USA","institution_ids":["https://openalex.org/I24603500"]},{"raw_affiliation_string":"Department of Mathematics and Statistics","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics and Computer Science Santa Clara University Santa Clara, California, USA","institution_ids":["https://openalex.org/I16269868"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089938106","display_name":"Byron L. Walden","orcid":null},"institutions":[{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]},{"id":"https://openalex.org/I16269868","display_name":"Santa Clara University","ror":"https://ror.org/03ypqe447","country_code":"US","type":"education","lineage":["https://openalex.org/I16269868"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Byron L. Walden","raw_affiliation_strings":["Department of Mathematics and Statistics","Department of Mathematics and Computer Science Santa Clara University Santa Clara, California, USA","University of Massachusetts Amherst, Massachusetts, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics and Computer Science Santa Clara University Santa Clara, California, USA","institution_ids":["https://openalex.org/I16269868"]},{"raw_affiliation_string":"University of Massachusetts Amherst, Massachusetts, USA","institution_ids":["https://openalex.org/I24603500"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5016465722"],"corresponding_institution_ids":["https://openalex.org/I16269868","https://openalex.org/I24603500"],"apc_list":null,"apc_paid":null,"fwci":0.8718,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.6793401,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"14","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9994999766349792,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9993000030517578,"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/T10849","display_name":"Finite Group Theory Research","score":0.9990000128746033,"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/mathematics","display_name":"Mathematics","score":0.892219603061676},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7613072395324707},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6022809147834778},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5956510305404663},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.5450731515884399},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"Symmetric group","score":0.4913925230503082},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4214520752429962},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36142241954803467},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0439169704914093}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.892219603061676},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7613072395324707},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6022809147834778},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5956510305404663},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.5450731515884399},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.4913925230503082},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4214520752429962},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36142241954803467},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0439169704914093},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/961","is_oa":true,"landing_page_url":"https://doi.org/10.37236/961","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1r43/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:scholarworks.umass.edu:20.500.14394/34641","is_oa":false,"landing_page_url":"https://hdl.handle.net/20.500.14394/34641","pdf_url":null,"source":{"id":"https://openalex.org/S4306402057","display_name":"Scholarworks (University of Massachusetts Amherst)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I24603500","host_organization_name":"University of Massachusetts Amherst","host_organization_lineage":["https://openalex.org/I24603500"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"published","raw_type":"article"},{"id":"pmh:oai:scholarworks.umass.edu:math_faculty_pubs-1396","is_oa":false,"landing_page_url":"https://scholarworks.umass.edu/math_faculty_pubs/397","pdf_url":null,"source":{"id":"https://openalex.org/S4306402057","display_name":"Scholarworks (University of Massachusetts Amherst)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I24603500","host_organization_name":"University of Massachusetts Amherst","host_organization_lineage":["https://openalex.org/I24603500"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics and Statistics Department Faculty Publication Series","raw_type":"text"},{"id":"pmh:oai:works.bepress.com:paul_gunnells-1012","is_oa":false,"landing_page_url":"https://works.bepress.com/paul_gunnells/13","pdf_url":null,"source":{"id":"https://openalex.org/S4306402240","display_name":"ScholarWorks@UMassAmherst (University of Massachusetts Amherst)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I24603500","host_organization_name":"University of Massachusetts Amherst","host_organization_lineage":["https://openalex.org/I24603500"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Paul Gunnells","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/961","is_oa":true,"landing_page_url":"https://doi.org/10.37236/961","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1r43/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":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320311294","display_name":"Santa Clara University","ror":"https://ror.org/03ypqe447"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1874018431.pdf","grobid_xml":"https://content.openalex.org/works/W1874018431.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W141723088","https://openalex.org/W1969083090","https://openalex.org/W2058006306","https://openalex.org/W2106079666","https://openalex.org/W2166435158","https://openalex.org/W6664873925"],"related_works":["https://openalex.org/W2001036795","https://openalex.org/W2154748900","https://openalex.org/W2474979212","https://openalex.org/W3093811938","https://openalex.org/W2114191958","https://openalex.org/W257950053","https://openalex.org/W2062626603","https://openalex.org/W2087351849","https://openalex.org/W2952745759","https://openalex.org/W2069948527"],"abstract_inverted_index":{"We":[0],"compute":[1],"the":[2,5,9,15,21,44,51,56],"spectrum":[3,34],"of":[4,8,25,43,55,64],"Schreier":[6],"graph":[7],"symmetric":[10],"group":[11],"$S_n$":[12],"corresponding":[13],"to":[14],"Young":[16],"subgroup":[17],"$S_2\\times":[18],"S_{n-2}$":[19],"and":[20,37],"generating":[22],"set":[23],"consisting":[24],"initial":[26],"reversals.":[27],"In":[28],"particular,":[29],"we":[30],"show":[31],"that":[32,50],"this":[33,62],"is":[35,49,58],"integral":[36],"for":[38,61],"$n\\geq":[39],"8$":[40],"consists":[41],"precisely":[42],"integers":[45],"$\\{0,1,\\ldots,n\\}$.":[46],"A":[47],"consequence":[48],"first":[52],"positive":[53],"eigenvalue":[54],"Laplacian":[57],"always":[59],"$1$":[60],"family":[63],"graphs.":[65]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}