{"id":"https://openalex.org/W2119910227","doi":"https://doi.org/10.37236/2955","title":"Fixed Point Polynomials of Permutation Groups","display_name":"Fixed Point Polynomials of Permutation Groups","publication_year":2013,"publication_date":"2013-05-09","ids":{"openalex":"https://openalex.org/W2119910227","doi":"https://doi.org/10.37236/2955","mag":"2119910227"},"language":"en","primary_location":{"id":"doi:10.37236/2955","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2955","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p26/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/v20i2p26/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5097611907","display_name":"Clarence Harden","orcid":null},"institutions":[{"id":"https://openalex.org/I110002522","display_name":"University of Essex","ror":"https://ror.org/02nkf1q06","country_code":"GB","type":"education","lineage":["https://openalex.org/I110002522"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"C. M. Harden","raw_affiliation_strings":["University of Essex","University of Essex **"],"affiliations":[{"raw_affiliation_string":"University of Essex","institution_ids":["https://openalex.org/I110002522"]},{"raw_affiliation_string":"University of Essex **","institution_ids":["https://openalex.org/I110002522"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057789509","display_name":"David Penman","orcid":null},"institutions":[{"id":"https://openalex.org/I110002522","display_name":"University of Essex","ror":"https://ror.org/02nkf1q06","country_code":"GB","type":"education","lineage":["https://openalex.org/I110002522"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"D. B. Penman","raw_affiliation_strings":["University of Essex","University of Essex **"],"affiliations":[{"raw_affiliation_string":"University of Essex","institution_ids":["https://openalex.org/I110002522"]},{"raw_affiliation_string":"University of Essex **","institution_ids":["https://openalex.org/I110002522"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5097611907"],"corresponding_institution_ids":["https://openalex.org/I110002522"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.17269414,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"20","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9976999759674072,"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/permutation","display_name":"Permutation (music)","score":0.7679687738418579},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7539872527122498},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7485600113868713},{"id":"https://openalex.org/keywords/derangement","display_name":"Derangement","score":0.619250476360321},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.604804515838623},{"id":"https://openalex.org/keywords/permutation-group","display_name":"Permutation group","score":0.5666881799697876},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"Symmetric group","score":0.542790412902832},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5159571766853333},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.47962722182273865},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.4770171642303467},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46699395775794983},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4188939929008484},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3828926682472229},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11236023902893066},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05016288161277771}],"concepts":[{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.7679687738418579},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7539872527122498},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7485600113868713},{"id":"https://openalex.org/C38298161","wikidata":"https://www.wikidata.org/wiki/Q1207920","display_name":"Derangement","level":2,"score":0.619250476360321},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.604804515838623},{"id":"https://openalex.org/C92957085","wikidata":"https://www.wikidata.org/wiki/Q1412905","display_name":"Permutation group","level":3,"score":0.5666881799697876},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.542790412902832},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5159571766853333},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.47962722182273865},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.4770171642303467},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46699395775794983},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4188939929008484},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3828926682472229},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11236023902893066},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05016288161277771},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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":1,"locations":[{"id":"doi:10.37236/2955","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2955","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p26/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"}],"best_oa_location":{"id":"doi:10.37236/2955","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2955","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p26/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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2119910227.pdf","grobid_xml":"https://content.openalex.org/works/W2119910227.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W1501381924","https://openalex.org/W1519229378","https://openalex.org/W1754421315","https://openalex.org/W1777511937","https://openalex.org/W1968428228","https://openalex.org/W1969474871","https://openalex.org/W2001719686","https://openalex.org/W2009398469","https://openalex.org/W2019885050","https://openalex.org/W2036185248","https://openalex.org/W2041902240","https://openalex.org/W2063850651","https://openalex.org/W2064405705","https://openalex.org/W2086995486","https://openalex.org/W2090590511","https://openalex.org/W2103995763","https://openalex.org/W2115090518","https://openalex.org/W2138429661","https://openalex.org/W2149149668","https://openalex.org/W2169273991","https://openalex.org/W2313394528","https://openalex.org/W2316033594","https://openalex.org/W2321225259","https://openalex.org/W2911541580","https://openalex.org/W3043060850","https://openalex.org/W3098500254","https://openalex.org/W3201162018","https://openalex.org/W4240854333","https://openalex.org/W4241604094","https://openalex.org/W4244425032"],"related_works":["https://openalex.org/W2769202988","https://openalex.org/W4298457394","https://openalex.org/W2963471363","https://openalex.org/W2338752714","https://openalex.org/W2022866443","https://openalex.org/W2139825306","https://openalex.org/W3101611711","https://openalex.org/W3013156496","https://openalex.org/W3099520598","https://openalex.org/W4251766710"],"abstract_inverted_index":{"In":[0,36],"this":[1,108,115],"paper":[2,116],"we":[3,38],"study,":[4],"given":[5],"a":[6,12,54],"group":[7,97],"$G$":[8,29],"of":[9,11,26,46,57,79,90,107],"permutations":[10,27],"finite":[13],"set,":[14],"the":[15,24,47,65,96],"so-called":[16],"fixed":[17,34],"point":[18],"polynomial":[19],"$\\sum_{i=0}^{n}f_{i}x^{i}$,":[20],"where":[21],"$f_{i}$":[22],"is":[23],"number":[25],"in":[28],"which":[30],"have":[31,82],"exactly":[32],"$i$":[33],"points.":[35],"particular,":[37],"investigate":[39],"how":[40],"root":[41],"location":[42],"relates":[43],"to":[44,64,114],"properties":[45],"permutation":[48],"group.":[49],"We":[50,74,86,100],"show":[51,87],"that":[52,76,88],"for":[53],"large":[55],"family":[56],"such":[58,80],"groups":[59],"most":[60],"roots":[61],"are":[62,93],"close":[63,101],"unit":[66],"circle":[67],"and":[68],"roughly":[69],"uniformly":[70],"distributed":[71],"round":[72],"it.":[73],"prove":[75],"many":[77,89],"families":[78],"polynomials":[81,92],"few":[83],"real":[84],"roots.":[85],"these":[91],"irreducible":[94],"when":[95],"acts":[98],"transitively.":[99],"by":[102],"indicating":[103],"some":[104],"future":[105],"directions":[106],"research.":[109],"A":[110],"corrigendum":[111],"was":[112],"appended":[113],"on":[117],"10th":[118],"October":[119],"2014.":[120]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
