{"id":"https://openalex.org/W7202204367","doi":"https://doi.org/10.48550/arxiv.2608.09078","title":"$q$-Difference Equations for two classes of Pattern Avoiding Permutations","display_name":"$q$-Difference Equations for two classes of Pattern Avoiding Permutations","publication_year":2026,"publication_date":"2026-08-10","ids":{"openalex":"https://openalex.org/W7202204367","doi":"https://doi.org/10.48550/arxiv.2608.09078"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2608.09078","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.09078","pdf_url":"https://arxiv.org/pdf/2608.09078","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/2608.09078","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006276965","display_name":"Paul Zinn-Justin","orcid":"https://orcid.org/0000-0002-6201-9562","observed_orcids":["https://orcid.org/0000-0002-6201-9562"]},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"The University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Zinn-Justin, Paul","raw_affiliation_strings":["SCHOOL OF MATHEMATICS AND STATISTICS , THE UNIVERSITY OF MELBOURNE , VICTORIA 3010 , AUSTRALIA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SCHOOL OF MATHEMATICS AND STATISTICS , THE UNIVERSITY OF MELBOURNE , VICTORIA 3010 , AUSTRALIA","institution_ids":["https://openalex.org/I165779595"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5006276965"],"corresponding_institution_ids":["https://openalex.org/I165779595"],"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9994999766349792,"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":0.9994999766349792,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.0003000000142492354,"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/T11567","display_name":"semigroups and automata theory","score":0.0,"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/pattern-avoiding-permutations","display_name":"pattern-avoiding permutations","score":0.8339999914169312},{"id":"https://openalex.org/keywords/q-difference-equations","display_name":"q-difference equations","score":0.875},{"id":"https://openalex.org/keywords/generating-functions","display_name":"generating functions","score":0.8230000138282776},{"id":"https://openalex.org/keywords/asymptotic-enumeration","display_name":"asymptotic enumeration","score":0.9419999718666077}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5974000096321106},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.5770000219345093},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5282999873161316},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42179998755455017},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3668999969959259},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.3506999909877777},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3034000098705292},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2847000062465668},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2815999984741211},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.25940001010894775},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2547000050544739},{"id":"https://openalex.org/C200985842","wikidata":"https://www.wikidata.org/wiki/Q3375503","display_name":"Random permutation","level":3,"score":0.25110000371932983}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.09078","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.09078","pdf_url":"https://arxiv.org/pdf/2608.09078","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.2608.09078","doi":"https://doi.org/10.48550/arxiv.2608.09078","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.09078","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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.09078","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.09078","pdf_url":"https://arxiv.org/pdf/2608.09078","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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7202204367.pdf","grobid_xml":"https://content.openalex.org/works/W7202204367.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,8],"study":[1],"the":[2,10,26],"nested":[3],"permutation":[4],"classes":[5],"$Av(4123,4231,4312)\\subset":[6],"Av(4123,4312)$.":[7],"relate":[9],"corresponding":[11],"generating":[12],"functions":[13,28],"$D^{(2)}(z)$,":[14],"$D^{(3)}(z)$":[15],"to":[16,23],"$q$-difference":[17],"equations.":[18],"Solving":[19],"these":[20],"equations":[21],"allows":[22],"show":[24],"that":[25,33],"generation":[27],"are":[29],"not":[30],"D-finite,":[31],"and":[32],"$[z^n]D^{(3)}(z)\\sim":[34],"0.0189672325071988\\ldots\\,":[35],"(4.46840899160393\\ldots)^n$,":[36],"$[z^n]D^{(2)}(z)\\sim0.0849833632890843\\ldots\\,":[37],"(3+2\\sqrt2)^n":[38],"n^{-3/2}$.":[39]},"counts_by_year":[],"updated_date":"2026-10-07T09:51:55.459714","created_date":"2026-08-12T00:00:00"}