{"id":"https://openalex.org/W4284678425","doi":"https://doi.org/10.1145/3476446.3535481","title":"Existence of Quantum Symmetries for Graphs on Up to Seven Vertices","display_name":"Existence of Quantum Symmetries for Graphs on Up to Seven Vertices","publication_year":2022,"publication_date":"2022-07-04","ids":{"openalex":"https://openalex.org/W4284678425","doi":"https://doi.org/10.1145/3476446.3535481"},"language":"en","primary_location":{"id":"doi:10.1145/3476446.3535481","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3476446.3535481","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://researchprofiles.ku.dk/files/338545560/EXISTENCE_OF_QUANTUM_SYMMETRIES.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059697607","display_name":"Viktor Levandovskyy","orcid":null},"institutions":[{"id":"https://openalex.org/I106157433","display_name":"University of Kassel","ror":"https://ror.org/04zc7p361","country_code":"DE","type":"education","lineage":["https://openalex.org/I106157433"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Viktor Levandovskyy","raw_affiliation_strings":["University of Kassel, Kassel, Germany"],"affiliations":[{"raw_affiliation_string":"University of Kassel, Kassel, Germany","institution_ids":["https://openalex.org/I106157433"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027815561","display_name":"Christian Eder","orcid":"https://orcid.org/0000-0002-8814-8493"},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christian Eder","raw_affiliation_strings":["TU Kaiserslautern, Kaiserslautern, Germany"],"affiliations":[{"raw_affiliation_string":"TU Kaiserslautern, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072945611","display_name":"Andreas Steenpa\u00df","orcid":null},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Andreas Steenpass","raw_affiliation_strings":["TU Kaiserslautern, Kaiserslautern, Germany"],"affiliations":[{"raw_affiliation_string":"TU Kaiserslautern, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103175989","display_name":"Simon Schmidt","orcid":"https://orcid.org/0000-0002-4863-5318"},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Simon Schmidt","raw_affiliation_strings":["University of Copenhagen, Copenhagen, Denmark"],"affiliations":[{"raw_affiliation_string":"University of Copenhagen, Copenhagen, Denmark","institution_ids":["https://openalex.org/I124055696"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035445344","display_name":"Julien Schanz","orcid":"https://orcid.org/0009-0005-6562-8442"},"institutions":[{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Julien Schanz","raw_affiliation_strings":["Saarland University, Saarbr\u00fccken, Germany"],"affiliations":[{"raw_affiliation_string":"Saarland University, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I91712215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021449152","display_name":"Moritz Weber","orcid":"https://orcid.org/0000-0002-1810-6343"},"institutions":[{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Moritz Weber","raw_affiliation_strings":["Saarland University, Saarbr\u00fccken, Germany"],"affiliations":[{"raw_affiliation_string":"Saarland University, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I91712215"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5059697607"],"corresponding_institution_ids":["https://openalex.org/I106157433"],"apc_list":null,"apc_paid":null,"fwci":1.6073,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.81975395,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"311","last_page":"318"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9998999834060669,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9998999834060669,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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":0.9997000098228455,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.6777213215827942},{"id":"https://openalex.org/keywords/noncommutative-geometry","display_name":"Noncommutative geometry","score":0.5711581707000732},{"id":"https://openalex.org/keywords/graph-automorphism","display_name":"Graph automorphism","score":0.5707715749740601},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5697416067123413},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.5128934383392334},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.5097112059593201},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4960847795009613},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4754238426685333},{"id":"https://openalex.org/keywords/symmetric-graph","display_name":"Symmetric graph","score":0.46827104687690735},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4073725640773773},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36521831154823303},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3242914080619812},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.24497777223587036},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.201680988073349},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.19859272241592407},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17713859677314758}],"concepts":[{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.6777213215827942},{"id":"https://openalex.org/C68797384","wikidata":"https://www.wikidata.org/wiki/Q2746792","display_name":"Noncommutative geometry","level":2,"score":0.5711581707000732},{"id":"https://openalex.org/C6049932","wikidata":"https://www.wikidata.org/wiki/Q834981","display_name":"Graph automorphism","level":5,"score":0.5707715749740601},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5697416067123413},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.5128934383392334},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5097112059593201},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4960847795009613},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4754238426685333},{"id":"https://openalex.org/C14201764","wikidata":"https://www.wikidata.org/wiki/Q1205074","display_name":"Symmetric graph","level":5,"score":0.46827104687690735},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4073725640773773},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36521831154823303},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3242914080619812},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.24497777223587036},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.201680988073349},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.19859272241592407},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17713859677314758},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3476446.3535481","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3476446.3535481","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/9cd549da-e897-4b8b-ba0a-9d035ef3f85f","is_oa":true,"landing_page_url":"https://researchprofiles.ku.dk/da/publications/9cd549da-e897-4b8b-ba0a-9d035ef3f85f","pdf_url":"https://researchprofiles.ku.dk/files/338545560/EXISTENCE_OF_QUANTUM_SYMMETRIES.pdf","source":{"id":"https://openalex.org/S4306401983","display_name":"Research at the University of Copenhagen (University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I124055696","host_organization_name":"University of Copenhagen","host_organization_lineage":["https://openalex.org/I124055696"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Levandovskyy , V , Eder , C , Steenpass , A , Schmidt , S , Schanz , J & Weber , M 2022 , Existence of Quantum Symmetries for Graphs on Up to Seven Vertices : A Computer based Approach . in ISSAC '22: Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation . ACM Association for Computing Machinery , pp. 311-318 , 2022 International Symposium on Symbolic and Algebraic Computation - ISSAC '22 , Villeneuve-d'Ascq , France , 04/07/2022 . https://doi.org/10.1145/3476446.3535481","raw_type":"contributionToPeriodical"}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/9cd549da-e897-4b8b-ba0a-9d035ef3f85f","is_oa":true,"landing_page_url":"https://researchprofiles.ku.dk/da/publications/9cd549da-e897-4b8b-ba0a-9d035ef3f85f","pdf_url":"https://researchprofiles.ku.dk/files/338545560/EXISTENCE_OF_QUANTUM_SYMMETRIES.pdf","source":{"id":"https://openalex.org/S4306401983","display_name":"Research at the University of Copenhagen (University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I124055696","host_organization_name":"University of Copenhagen","host_organization_lineage":["https://openalex.org/I124055696"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Levandovskyy , V , Eder , C , Steenpass , A , Schmidt , S , Schanz , J & Weber , M 2022 , Existence of Quantum Symmetries for Graphs on Up to Seven Vertices : A Computer based Approach . in ISSAC '22: Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation . ACM Association for Computing Machinery , pp. 311-318 , 2022 International Symposium on Symbolic and Algebraic Computation - ISSAC '22 , Villeneuve-d'Ascq , France , 04/07/2022 . https://doi.org/10.1145/3476446.3535481","raw_type":"contributionToPeriodical"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G686766967","display_name":null,"funder_award_id":"SFB-TRR 195 ?Symbolic Tools in Mathematics and their Application?","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4284678425.pdf","grobid_xml":"https://content.openalex.org/works/W4284678425.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1801637858","https://openalex.org/W2037328702","https://openalex.org/W2060402408","https://openalex.org/W2106837101","https://openalex.org/W2320948793","https://openalex.org/W2596472521","https://openalex.org/W2729907698","https://openalex.org/W2769166518","https://openalex.org/W2949938216","https://openalex.org/W3018166064","https://openalex.org/W3037224393","https://openalex.org/W3045732501","https://openalex.org/W3101939560","https://openalex.org/W4252290972","https://openalex.org/W6763714385"],"related_works":["https://openalex.org/W1663451455","https://openalex.org/W1955707229","https://openalex.org/W3100920062","https://openalex.org/W4394667031","https://openalex.org/W3156064174","https://openalex.org/W2034563384","https://openalex.org/W3125006187","https://openalex.org/W2782009743","https://openalex.org/W2746425405","https://openalex.org/W2072644539"],"abstract_inverted_index":{"The":[0,64],"symmetries":[1,34,44,46,104],"of":[2,15,21,35,102,134,145],"a":[3,19,22,50,61,130],"finite":[4],"graph":[5],"are":[6,41],"described":[7],"by":[8,29],"its":[9],"automorphism":[10,24,77,132],"group;":[11],"in":[12,86],"the":[13,32,36,58,70,75,92,100,143],"setting":[14],"Woronowicz's":[16],"quantum":[17,23,33,43,76,103,146],"groups,":[18],"notion":[20],"group":[25,78,133],"has":[26],"been":[27],"defined":[28],"Banica":[30],"capturing":[31],"graph.":[37],"In":[38],"general,":[39],"there":[40],"more":[42],"than":[45],"and":[47,96,113],"it":[48],"is":[49,57,66,79,139],"non-trivial":[51],"task":[52],"to":[53,74,88,118],"determine":[54,99],"when":[55],"this":[56,90],"case":[59],"for":[60,105,116,142],"given":[62],"graph:":[63],"question":[65],"whether":[67],"or":[68,137],"not":[69],"associative":[71],"algebra":[72],"associated":[73],"commutative.":[80],"We":[81,98],"use":[82],"noncommutative":[83],"Gr\u00f6bner":[84],"bases":[85],"order":[87,135],"tackle":[89],"problem;":[91],"implementation":[93],"uses":[94],"Gap":[95],"Singular:Letterplace.":[97],"existence":[101,144],"all":[106],"connected,":[107],"undirected":[108],"graphs":[109],"without":[110,114],"multiple":[111],"edges":[112],"self-edges,":[115],"up":[117],"seven":[119],"vertices.":[120],"As":[121],"an":[122,140],"outcome,":[123],"we":[124],"infer":[125],"within":[126],"our":[127],"regime":[128],"that":[129],"classical":[131],"one":[136],"two":[138],"obstruction":[141],"symmetries.":[147]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
