{"id":"https://openalex.org/W1892915578","doi":"https://doi.org/10.37236/1096","title":"The Maximum Distinguishing Number of a Group","display_name":"The Maximum Distinguishing Number of a Group","publication_year":2006,"publication_date":"2006-08-07","ids":{"openalex":"https://openalex.org/W1892915578","doi":"https://doi.org/10.37236/1096","mag":"1892915578"},"language":"en","primary_location":{"id":"doi:10.37236/1096","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1096","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r70/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/v13i1r70/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020887417","display_name":"Melody Chan","orcid":null},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Melody Chan","raw_affiliation_strings":["Princeton University Princeton, New Jersey, USA"],"affiliations":[{"raw_affiliation_string":"Princeton University Princeton, New Jersey, USA","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5020887417"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":4.3812,"has_fulltext":true,"cited_by_count":34,"citation_normalized_percentile":{"value":0.94309087,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"13","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9998000264167786,"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":0.9664000272750854,"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/mathematics","display_name":"Mathematics","score":0.9151824712753296},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8478453755378723},{"id":"https://openalex.org/keywords/square-free-integer","display_name":"Square-free integer","score":0.655056357383728},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.6423317193984985},{"id":"https://openalex.org/keywords/nilpotent","display_name":"Nilpotent","score":0.6014701128005981},{"id":"https://openalex.org/keywords/permutation-group","display_name":"Permutation group","score":0.5408918857574463},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.4933291971683502},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4885765016078949},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3824925422668457}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9151824712753296},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8478453755378723},{"id":"https://openalex.org/C188139237","wikidata":"https://www.wikidata.org/wiki/Q50706","display_name":"Square-free integer","level":2,"score":0.655056357383728},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.6423317193984985},{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.6014701128005981},{"id":"https://openalex.org/C92957085","wikidata":"https://www.wikidata.org/wiki/Q1412905","display_name":"Permutation group","level":3,"score":0.5408918857574463},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.4933291971683502},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4885765016078949},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3824925422668457},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/1096","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1096","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r70/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:10.1.1.88.6818","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.88.6818","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_13/PDF/v13i1r70.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1096","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1096","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r70/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":[{"id":"https://openalex.org/G6507447573","display_name":null,"funder_award_id":"several","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G652434006","display_name":"REU Site: An Undergraduate Research Experience Program in Discrete Mathematics","funder_award_id":"0137611","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","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"},{"id":"https://openalex.org/F4320308380","display_name":"Yale University","ror":"https://ror.org/03v76x132"},{"id":"https://openalex.org/F4320309636","display_name":"University of Minnesota","ror":"https://ror.org/03grvy078"},{"id":"https://openalex.org/F4320311089","display_name":"National Security Agency","ror":"https://ror.org/0047bvr32"},{"id":"https://openalex.org/F4320311500","display_name":"University of Minnesota Duluth","ror":"https://ror.org/01hy4qx27"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1892915578.pdf","grobid_xml":"https://content.openalex.org/works/W1892915578.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W425144646","https://openalex.org/W1855706715","https://openalex.org/W2003755322","https://openalex.org/W2012186425","https://openalex.org/W2095694257","https://openalex.org/W2153525410","https://openalex.org/W2154745345","https://openalex.org/W2167676258","https://openalex.org/W2169476811","https://openalex.org/W2953162523"],"related_works":["https://openalex.org/W4362598163","https://openalex.org/W209367526","https://openalex.org/W2506973052","https://openalex.org/W368092084","https://openalex.org/W4320165426","https://openalex.org/W4366206987","https://openalex.org/W2041699698","https://openalex.org/W4251766710","https://openalex.org/W2349665798","https://openalex.org/W3013156496"],"abstract_inverted_index":{"Let":[0],"$G$":[1,18,55,67],"be":[2],"a":[3,8,33,43,113],"group":[4,40,110],"acting":[5],"faithfully":[6],"on":[7,19,116],"set":[9],"$X$.":[10,47],"The":[11],"distinguishing":[12,71,84,101],"number":[13,26,72,85,102],"of":[14,17,27,35,46,58,63,93,103,106],"the":[15,24,100,104,107,117],"action":[16,105],"$X$,":[20],"denoted":[21],"$D_G(X)$,":[22],"is":[23,56,121],"smallest":[25],"colors":[28],"such":[29],"that":[30,53,78,99],"there":[31],"exists":[32],"coloring":[34],"$X$":[36],"where":[37],"no":[38],"nontrivial":[39],"element":[41],"induces":[42],"color-preserving":[44],"permutation":[45],"In":[48],"this":[49],"paper,":[50],"we":[51],"show":[52],"if":[54,123],"nilpotent":[57],"class":[59],"$c$":[60,65],"or":[61],"supersolvable":[62],"length":[64],"then":[66],"always":[68],"acts":[69],"with":[70,83],"at":[73,86,126],"most":[74,87],"$c+1$.":[75],"We":[76,96],"obtain":[77],"all":[79,91],"metacyclic":[80],"groups":[81,92],"act":[82],"3;":[88],"these":[89],"include":[90],"squarefree":[94],"order.":[95],"also":[97],"prove":[98],"general":[108],"linear":[109],"$GL_n(K)$":[111],"over":[112],"field":[114],"$K$":[115,124],"vector":[118],"space":[119],"$K^n$":[120],"2":[122],"has":[125],"least":[127],"$n+1$":[128],"elements.":[129]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}