{"id":"https://openalex.org/W7213528828","doi":"https://doi.org/10.48550/arxiv.2609.19078","title":"Simple Cayley permutations","display_name":"Simple Cayley permutations","publication_year":2026,"publication_date":"2026-09-16","ids":{"openalex":"https://openalex.org/W7213528828","doi":"https://doi.org/10.48550/arxiv.2609.19078"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.19078","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.19078","pdf_url":"https://arxiv.org/pdf/2609.19078","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.19078","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015643450","display_name":"Giulio Cerbai","orcid":"https://orcid.org/0000-0002-7020-4020","observed_orcids":["https://orcid.org/0000-0002-7020-4020"]},"institutions":[{"id":"https://openalex.org/I165368041","display_name":"University of Iceland","ror":"https://ror.org/01db6h964","country_code":"IS","type":"education","lineage":["https://openalex.org/I165368041"]}],"countries":["IS"],"is_corresponding":false,"raw_author_name":"Cerbai, Giulio","raw_affiliation_strings":["Department of Mathematics University of Iceland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Iceland","institution_ids":["https://openalex.org/I165368041"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034916191","display_name":"Anders Claesson","orcid":"https://orcid.org/0000-0001-5797-8673","observed_orcids":["https://orcid.org/0000-0001-5797-8673"]},"institutions":[{"id":"https://openalex.org/I165368041","display_name":"University of Iceland","ror":"https://ror.org/01db6h964","country_code":"IS","type":"education","lineage":["https://openalex.org/I165368041"]}],"countries":["IS"],"is_corresponding":false,"raw_author_name":"Claesson, Anders","raw_affiliation_strings":["Department of Mathematics University of Iceland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Iceland","institution_ids":["https://openalex.org/I165368041"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I165368041"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9976000189781189,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9976000189781189,"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/T11567","display_name":"semigroups and automata theory","score":0.0010999999940395355,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.00039999998989515007,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/simple-permutations","display_name":"simple permutations","score":0.8709999918937683},{"id":"https://openalex.org/keywords/inflation","display_name":"inflation","score":0.5120000243186951},{"id":"https://openalex.org/keywords/indecomposability","display_name":"indecomposability","score":0.7649999856948853},{"id":"https://openalex.org/keywords/relational-structures","display_name":"relational structures","score":0.5860000252723694},{"id":"https://openalex.org/keywords/modules","display_name":"modules","score":0.6949999928474426},{"id":"https://openalex.org/keywords/enumeration","display_name":"enumeration","score":0.7509999871253967}],"concepts":[{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.8104000091552734},{"id":"https://openalex.org/C120204988","wikidata":"https://www.wikidata.org/wiki/Q859174","display_name":"Cayley graph","level":3,"score":0.7965999841690063},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7505999803543091},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.7455999851226807},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6560999751091003},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6134999990463257},{"id":"https://openalex.org/C2778220771","wikidata":"https://www.wikidata.org/wiki/Q1522579","display_name":"Substitution (logic)","level":2,"score":0.5424000024795532},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5393000245094299},{"id":"https://openalex.org/C18586221","wikidata":"https://www.wikidata.org/wiki/Q2778065","display_name":"Cayley transform","level":5,"score":0.5167999863624573},{"id":"https://openalex.org/C18116961","wikidata":"https://www.wikidata.org/wiki/Q734209","display_name":"Generating set of a group","level":2,"score":0.46860000491142273},{"id":"https://openalex.org/C4093544","wikidata":"https://www.wikidata.org/wiki/Q179208","display_name":"Cayley's theorem","level":5,"score":0.4422000050544739},{"id":"https://openalex.org/C2776372474","wikidata":"https://www.wikidata.org/wiki/Q508291","display_name":"Simplicity","level":2,"score":0.4327000081539154},{"id":"https://openalex.org/C64137656","wikidata":"https://www.wikidata.org/wiki/Q1064405","display_name":"Parity of a permutation","level":4,"score":0.42239999771118164},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3977999985218048},{"id":"https://openalex.org/C92957085","wikidata":"https://www.wikidata.org/wiki/Q1412905","display_name":"Permutation group","level":3,"score":0.39340001344680786},{"id":"https://openalex.org/C63388996","wikidata":"https://www.wikidata.org/wiki/Q1340623","display_name":"Classification of finite simple groups","level":4,"score":0.3862000107765198},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.3831000030040741},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.3553999960422516},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3188999891281128},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.30140000581741333},{"id":"https://openalex.org/C77670614","wikidata":"https://www.wikidata.org/wiki/Q212130","display_name":"Cyclic permutation","level":3,"score":0.30090001225471497},{"id":"https://openalex.org/C81651864","wikidata":"https://www.wikidata.org/wiki/Q874429","display_name":"Group theory","level":2,"score":0.29120001196861267},{"id":"https://openalex.org/C54643580","wikidata":"https://www.wikidata.org/wiki/Q1005603","display_name":"Algebraic combinatorics","level":2,"score":0.2614000141620636},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2599000036716461}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.19078","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.19078","pdf_url":"https://arxiv.org/pdf/2609.19078","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.19078","doi":"https://doi.org/10.48550/arxiv.2609.19078","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.19078","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.19078","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.19078","pdf_url":"https://arxiv.org/pdf/2609.19078","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213528828.pdf","grobid_xml":"https://content.openalex.org/works/W7213528828.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W2267908133"],"related_works":["https://openalex.org/W2133320102","https://openalex.org/W7223337768","https://openalex.org/W1481142573","https://openalex.org/W7024639952","https://openalex.org/W4298348206","https://openalex.org/W7098804183","https://openalex.org/W2112942248","https://openalex.org/W7099022183","https://openalex.org/W1677848800","https://openalex.org/W2913306542"],"abstract_inverted_index":{"We":[0,30,51],"propose":[1],"a":[2,17,32],"notion":[3],"of":[4,26,38,46],"simplicity":[5],"for":[6],"Cayley":[7,57],"permutations":[8,58],"that":[9,37],"is":[10],"compatible":[11],"with":[12,21],"inflation":[13],"and":[14,28],"agrees,":[15],"under":[16],"natural":[18],"relational":[19,49],"encoding,":[20],"indecomposability":[22],"in":[23,40],"the":[24,42,47],"sense":[25],"Schmerl":[27],"Trotter.":[29],"establish":[31],"substitution":[33],"decomposition":[34],"analogous":[35],"to":[36,54],"permutations,":[39],"which":[41],"components":[43],"are":[44],"modules":[45],"associated":[48],"structure.":[50],"use":[52],"it":[53],"enumerate":[55],"simple":[56,62],"as":[59,61],"well":[60],"restricted":[63],"growth":[64],"functions.":[65]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-18T00:00:00"}