{"id":"https://openalex.org/W1570296778","doi":"https://doi.org/10.37236/2749","title":"A Note on Automorphisms of the Infinite-Dimensional Hypercube Graph","display_name":"A Note on Automorphisms of the Infinite-Dimensional Hypercube Graph","publication_year":2012,"publication_date":"2012-11-08","ids":{"openalex":"https://openalex.org/W1570296778","doi":"https://doi.org/10.37236/2749","mag":"1570296778"},"language":"en","primary_location":{"id":"doi:10.37236/2749","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2749","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i4p23/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/v19i4p23/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060769535","display_name":"Mark Pankov","orcid":"https://orcid.org/0000-0003-2052-0348"},"institutions":[{"id":"https://openalex.org/I47996466","display_name":"University of Warmia and Mazury in Olsztyn","ror":"https://ror.org/05s4feg49","country_code":"PL","type":"education","lineage":["https://openalex.org/I47996466"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Mark Pankov","raw_affiliation_strings":["Department of Mathematics and Computer Science,\r\nUniversity of Warmia and Mazury","Department of Mathematics and Computer Science,#R##N#University of Warmia and Mazury"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science,\r\nUniversity of Warmia and Mazury","institution_ids":["https://openalex.org/I47996466"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science,#R##N#University of Warmia and Mazury","institution_ids":["https://openalex.org/I47996466"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5060769535"],"corresponding_institution_ids":["https://openalex.org/I47996466"],"apc_list":null,"apc_paid":null,"fwci":0.3471,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.58916813,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"19","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9994000196456909,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9994000196456909,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10849","display_name":"Finite Group Theory Research","score":0.9958999752998352,"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/automorphism","display_name":"Automorphism","score":0.8792015314102173},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8030955791473389},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7904557585716248},{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.6765176057815552},{"id":"https://openalex.org/keywords/automorphism-group","display_name":"Automorphism group","score":0.6501408815383911},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6486260890960693},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5706946849822998},{"id":"https://openalex.org/keywords/hypercube-graph","display_name":"Hypercube graph","score":0.5594268441200256},{"id":"https://openalex.org/keywords/graph-automorphism","display_name":"Graph automorphism","score":0.513139545917511},{"id":"https://openalex.org/keywords/connected-component","display_name":"Connected component","score":0.5005631446838379},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4337083399295807},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.2576700448989868},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.24802923202514648}],"concepts":[{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.8792015314102173},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8030955791473389},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7904557585716248},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.6765176057815552},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.6501408815383911},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6486260890960693},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5706946849822998},{"id":"https://openalex.org/C80763892","wikidata":"https://www.wikidata.org/wiki/Q958394","display_name":"Hypercube graph","level":5,"score":0.5594268441200256},{"id":"https://openalex.org/C6049932","wikidata":"https://www.wikidata.org/wiki/Q834981","display_name":"Graph automorphism","level":5,"score":0.513139545917511},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.5005631446838379},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4337083399295807},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.2576700448989868},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.24802923202514648}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/2749","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2749","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i4p23/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:10.37236/2749","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2749","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i4p23/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/W1570296778.pdf","grobid_xml":"https://content.openalex.org/works/W1570296778.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W240203132","https://openalex.org/W1993454608","https://openalex.org/W2028415642","https://openalex.org/W2054286350","https://openalex.org/W2071953162","https://openalex.org/W2153142809","https://openalex.org/W2485530965","https://openalex.org/W4231748928"],"related_works":["https://openalex.org/W2010961105","https://openalex.org/W2058944243","https://openalex.org/W2390102552","https://openalex.org/W2020627187","https://openalex.org/W2101573191","https://openalex.org/W2171587471","https://openalex.org/W4254221886","https://openalex.org/W2898596373","https://openalex.org/W1914727321","https://openalex.org/W1570296778"],"abstract_inverted_index":{"We":[0,34],"define":[1],"the":[2,16,37,43,54,64,68],"infinite-dimensional":[3],"hypercube":[4],"graph":[5,9,24],"$H_{{\\aleph}_{0}}$":[6],"as":[7],"a":[8],"whose":[10],"vertex":[11],"set":[12],"is":[13,25],"formed":[14],"by":[15,48],"so-called":[17],"singular":[18,57],"subsets":[19],"of":[20,39,56,67],"${\\mathbb":[21,51],"Z}\\setminus\\{0\\}$.":[22],"This":[23],"not":[26],"connected,":[27],"but":[28],"it":[29],"has":[30],"isomorphic":[31],"connected":[32,44,69],"components.":[33,70],"show":[35],"that":[36],"restrictions":[38],"its":[40],"automorphisms":[41],"to":[42],"components":[45],"are":[46],"induced":[47],"permutations":[49],"on":[50],"Z}\\setminus\\{0\\}$":[52],"preserving":[53],"family":[55],"subsets.":[58],"As":[59],"an":[60],"application,":[61],"we":[62],"describe":[63],"automorphism":[65],"group":[66]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
