{"id":"https://openalex.org/W7213585149","doi":"https://doi.org/10.48550/arxiv.2609.20521","title":"Generation of Iterated Wreath Products Constructed from Full Transformation Monoids and Symmetric Groups","display_name":"Generation of Iterated Wreath Products Constructed from Full Transformation Monoids and Symmetric Groups","publication_year":2026,"publication_date":"2026-09-17","ids":{"openalex":"https://openalex.org/W7213585149","doi":"https://doi.org/10.48550/arxiv.2609.20521"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.20521","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20521","pdf_url":"https://arxiv.org/pdf/2609.20521","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.20521","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5125003636","display_name":"Jiaping Lu","orcid":"https://orcid.org/0009-0009-2102-5278","observed_orcids":["https://orcid.org/0009-0009-2102-5278"]},"institutions":[{"id":"https://openalex.org/I16835326","display_name":"University of St Andrews","ror":"https://ror.org/02wn5qz54","country_code":"GB","type":"education","lineage":["https://openalex.org/I16835326"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Lu, Jiaping","raw_affiliation_strings":["Mathematical Institute , University of St Andrews , North Haugh , St Andrews , Fife , KY16 9SS"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute , University of St Andrews , North Haugh , St Andrews , Fife , KY16 9SS","institution_ids":["https://openalex.org/I16835326"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5125003636"],"corresponding_institution_ids":["https://openalex.org/I16835326"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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/T11567","display_name":"semigroups and automata theory","score":0.9907000064849854,"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/T11567","display_name":"semigroups and automata theory","score":0.9907000064849854,"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/T10849","display_name":"Finite Group Theory Research","score":0.006800000090152025,"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/T12504","display_name":"Mathematics and Applications","score":0.0005000000237487257,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/iterated-wreath-products","display_name":"iterated wreath products","score":0.972000002861023},{"id":"https://openalex.org/keywords/full-transformation-monoid","display_name":"full transformation monoid","score":0.7009999752044678},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"symmetric group","score":1.0},{"id":"https://openalex.org/keywords/generating-sets","display_name":"generating sets","score":0.902999997138977},{"id":"https://openalex.org/keywords/transformation-semigroups","display_name":"transformation semigroups","score":0.9480000138282776}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8452000021934509},{"id":"https://openalex.org/C95635736","wikidata":"https://www.wikidata.org/wiki/Q1786640","display_name":"Wreath product","level":3,"score":0.8440999984741211},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.7962999939918518},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6055999994277954},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5636000037193298},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5486000180244446},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.5303000211715698},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.48840001225471497},{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.4860999882221222},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.4487000107765198},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34850001335144043},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3375000059604645},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.30820000171661377},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.27549999952316284}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.20521","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20521","pdf_url":"https://arxiv.org/pdf/2609.20521","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.2609.20521","doi":"https://doi.org/10.48550/arxiv.2609.20521","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.20521","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.20521","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20521","pdf_url":"https://arxiv.org/pdf/2609.20521","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/W7213585149.pdf","grobid_xml":"https://content.openalex.org/works/W7213585149.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7151864382","https://openalex.org/W2883022622","https://openalex.org/W1498595167","https://openalex.org/W1977841303","https://openalex.org/W2065346793","https://openalex.org/W1995408789","https://openalex.org/W2401275170","https://openalex.org/W2014389955","https://openalex.org/W4410244043","https://openalex.org/W2094512319"],"abstract_inverted_index":{"The":[0],"rank":[1,27],"of":[2,8,21,28,32],"a":[3,9],"semigroup":[4],"is":[5],"the":[6,26],"cardinality":[7],"smallest":[10],"generating":[11],"set.":[12],"In":[13],"this":[14],"paper,":[15],"we":[16],"introduce":[17],"iterated":[18,29],"wreath":[19,30],"products":[20,31],"transformation":[22,34],"semigroups.":[23],"We":[24],"determine":[25],"full":[33],"monoids":[35],"and":[36],"symmetric":[37],"groups.":[38]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-19T00:00:00"}