{"id":"https://openalex.org/W1550677861","doi":"https://doi.org/10.37236/341","title":"On Restricted Unitary Cayley Graphs and Symplectic Transformations Modulo $n$","display_name":"On Restricted Unitary Cayley Graphs and Symplectic Transformations Modulo $n$","publication_year":2010,"publication_date":"2010-05-07","ids":{"openalex":"https://openalex.org/W1550677861","doi":"https://doi.org/10.37236/341","mag":"1550677861"},"language":"en","primary_location":{"id":"doi:10.37236/341","is_oa":true,"landing_page_url":"https://doi.org/10.37236/341","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r69/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":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r69/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019353647","display_name":"Niel de Beaudrap","orcid":"https://orcid.org/0000-0001-9549-5146"},"institutions":[{"id":"https://openalex.org/I176453806","display_name":"University of Potsdam","ror":"https://ror.org/03bnmw459","country_code":"DE","type":"education","lineage":["https://openalex.org/I176453806"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Niel De Beaudrap","raw_affiliation_strings":["Quantum Information Theory Group Institut fr Physik und Astronomie, Universitt Potsdam","UNIVERSITY OF POTSDAM"],"affiliations":[{"raw_affiliation_string":"Quantum Information Theory Group Institut fr Physik und Astronomie, Universitt Potsdam","institution_ids":["https://openalex.org/I176453806"]},{"raw_affiliation_string":"UNIVERSITY OF POTSDAM","institution_ids":["https://openalex.org/I176453806"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019353647"],"corresponding_institution_ids":["https://openalex.org/I176453806"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.04655295,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"17","issue":"1","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":0.9998000264167786,"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":0.9998000264167786,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9995999932289124,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/cayley-graph","display_name":"Cayley graph","score":0.8096212148666382},{"id":"https://openalex.org/keywords/symplectic-matrix","display_name":"Symplectic matrix","score":0.7817630767822266},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.763248085975647},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.7106630206108093},{"id":"https://openalex.org/keywords/symplectic-representation","display_name":"Symplectic representation","score":0.6865129470825195},{"id":"https://openalex.org/keywords/symplectic-geometry","display_name":"Symplectic geometry","score":0.6833062171936035},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6068333983421326},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.530620813369751},{"id":"https://openalex.org/keywords/symplectic-group","display_name":"Symplectic group","score":0.48685067892074585},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.4770618975162506},{"id":"https://openalex.org/keywords/unitary-matrix","display_name":"Unitary matrix","score":0.4468838572502136},{"id":"https://openalex.org/keywords/quadratic-residue","display_name":"Quadratic residue","score":0.443888783454895},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42198559641838074},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.2667294144630432},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21453389525413513},{"id":"https://openalex.org/keywords/moment-map","display_name":"Moment map","score":0.1650262176990509}],"concepts":[{"id":"https://openalex.org/C120204988","wikidata":"https://www.wikidata.org/wiki/Q859174","display_name":"Cayley graph","level":3,"score":0.8096212148666382},{"id":"https://openalex.org/C185535465","wikidata":"https://www.wikidata.org/wiki/Q2705070","display_name":"Symplectic matrix","level":5,"score":0.7817630767822266},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.763248085975647},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.7106630206108093},{"id":"https://openalex.org/C104586451","wikidata":"https://www.wikidata.org/wiki/Q771008","display_name":"Symplectic representation","level":4,"score":0.6865129470825195},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.6833062171936035},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6068333983421326},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.530620813369751},{"id":"https://openalex.org/C175322374","wikidata":"https://www.wikidata.org/wiki/Q936434","display_name":"Symplectic group","level":3,"score":0.48685067892074585},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.4770618975162506},{"id":"https://openalex.org/C96214315","wikidata":"https://www.wikidata.org/wiki/Q727103","display_name":"Unitary matrix","level":3,"score":0.4468838572502136},{"id":"https://openalex.org/C12817185","wikidata":"https://www.wikidata.org/wiki/Q878259","display_name":"Quadratic residue","level":2,"score":0.443888783454895},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42198559641838074},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2667294144630432},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21453389525413513},{"id":"https://openalex.org/C40265840","wikidata":"https://www.wikidata.org/wiki/Q6897118","display_name":"Moment map","level":3,"score":0.1650262176990509},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.37236/341","is_oa":true,"landing_page_url":"https://doi.org/10.37236/341","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r69/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:arXiv.org:1002.0713","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1002.0713","pdf_url":"https://arxiv.org/pdf/1002.0713","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"mag:1550677861","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1002.0713v2","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.177.8920","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.177.8920","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_17/PDF/v17i1r69.pdf","raw_type":"text"},{"id":"pmh:oai:kobv.de-opus4-uni-potsdam:32122","is_oa":false,"landing_page_url":"https://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/32122","pdf_url":null,"source":{"id":"https://openalex.org/S4306400594","display_name":"publish.UP (University of Potsdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I176453806","host_organization_name":"University of Potsdam","host_organization_lineage":["https://openalex.org/I176453806"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"doi:10.48550/arxiv.1002.0713","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1002.0713","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.37236/341","is_oa":true,"landing_page_url":"https://doi.org/10.37236/341","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r69/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/W1550677861.pdf","grobid_xml":"https://content.openalex.org/works/W1550677861.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1973199140","https://openalex.org/W1983193381","https://openalex.org/W2015378916","https://openalex.org/W2019205401","https://openalex.org/W2046551711","https://openalex.org/W2058927760","https://openalex.org/W2099526591","https://openalex.org/W2137147061","https://openalex.org/W2142534064","https://openalex.org/W2950588511","https://openalex.org/W3111297213","https://openalex.org/W6636975353","https://openalex.org/W6640230470","https://openalex.org/W6642200229","https://openalex.org/W6643569721","https://openalex.org/W6654419961","https://openalex.org/W6654973255","https://openalex.org/W6675409862","https://openalex.org/W6685738324"],"related_works":["https://openalex.org/W2964138304","https://openalex.org/W1681935564","https://openalex.org/W3176213640","https://openalex.org/W3144474669","https://openalex.org/W1951746942","https://openalex.org/W3142861400","https://openalex.org/W1974619998","https://openalex.org/W1972541315","https://openalex.org/W2887851755","https://openalex.org/W2117498202","https://openalex.org/W2563768103","https://openalex.org/W3025291191","https://openalex.org/W2054119455","https://openalex.org/W2963768904","https://openalex.org/W2787253345","https://openalex.org/W2799884971","https://openalex.org/W1940303459","https://openalex.org/W2008857914","https://openalex.org/W2964014928","https://openalex.org/W2963254918"],"abstract_inverted_index":{"We":[0,29,100],"present":[1],"some":[2],"observations":[3],"on":[4,74,105],"a":[5,17,59,94,111],"restricted":[6],"variant":[7],"of":[8,19,21,66,77],"unitary":[9,32],"Cayley":[10,33],"graphs":[11,34],"modulo":[12,27,48],"$n$,":[13],"and":[14,44,53,86],"implications":[15],"for":[16,107],"decomposition":[18],"elements":[20],"symplectic":[22,83,95],"operators":[23],"over":[24,97],"the":[25,40,64,75,103],"integers":[26],"$n$.":[28],"define":[30],"quadratic":[31,60],"$G_n$,":[35],"whose":[36],"vertex":[37],"set":[38],"is":[39,58],"ring":[41],"${\\Bbb":[42,98],"Z}_n$,":[43],"where":[45],"residues":[46],"$a,b$":[47],"$n$":[49,106],"are":[50],"adjacent":[51],"if":[52,55],"only":[54],"their":[56],"difference":[57],"residue.":[61],"By":[62],"bounding":[63],"diameter":[65],"such":[67],"graphs,":[68],"we":[69],"show":[70],"an":[71],"upper":[72],"bound":[73],"number":[76],"elementary":[78],"operations":[79],"(symplectic":[80],"scalar":[81],"multiplications,":[82],"row":[84,87],"swaps,":[85],"additions":[88],"or":[89],"subtractions)":[90],"required":[91],"to":[92,109],"decompose":[93],"matrix":[96],"Z}_n$.":[99],"also":[101],"characterize":[102],"conditions":[104],"$G_n$":[108],"be":[110],"perfect":[112],"graph.":[113]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
