{"id":"https://openalex.org/W1490446672","doi":"https://doi.org/10.37236/1137","title":"Permutations, Cycles and the Pattern 2–13","display_name":"Permutations, Cycles and the Pattern 2–13","publication_year":2006,"publication_date":"2006-11-29","ids":{"openalex":"https://openalex.org/W1490446672","doi":"https://doi.org/10.37236/1137","mag":"1490446672"},"language":"en","primary_location":{"id":"doi:10.37236/1137","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1137","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r111/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":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r111/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003344434","display_name":"Robert Parviainen","orcid":null},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"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":"Robert Parviainen","raw_affiliation_strings":["ARC Centre of Excellence for Mathematics and Statistics of Complex Systems 139 Barry Street, The University of Melbourne, Victoria, 3010"],"affiliations":[{"raw_affiliation_string":"ARC Centre of Excellence for Mathematics and Statistics of Complex Systems 139 Barry Street, The University of Melbourne, Victoria, 3010","institution_ids":["https://openalex.org/I165779595"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5003344434"],"corresponding_institution_ids":["https://openalex.org/I165779595"],"apc_list":null,"apc_paid":null,"fwci":0.4689,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.55239787,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"13","issue":"1","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":0.9998999834060669,"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":0.9998999834060669,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.998199999332428,"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"}},{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/bijection","display_name":"Bijection","score":0.9013111591339111},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8496907949447632},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8427799940109253},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3202860653400421}],"concepts":[{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.9013111591339111},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8496907949447632},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8427799940109253},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3202860653400421}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/1137","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1137","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r111/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"}],"best_oa_location":{"id":"doi:10.37236/1137","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1137","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r111/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":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W1490446672.pdf"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1548412882","https://openalex.org/W2000355295","https://openalex.org/W2014724230","https://openalex.org/W2071829066","https://openalex.org/W2102348212","https://openalex.org/W2109846666","https://openalex.org/W4244594925","https://openalex.org/W6675798288"],"related_works":["https://openalex.org/W4287020903","https://openalex.org/W2952259524","https://openalex.org/W2279732055","https://openalex.org/W2995857455","https://openalex.org/W4288805235","https://openalex.org/W2998840281","https://openalex.org/W2027277382","https://openalex.org/W1508013399","https://openalex.org/W3181135859","https://openalex.org/W4302399754"],"abstract_inverted_index":{"We":[0],"count":[1],"the":[2,19],"number":[3,20],"of":[4,6,9,21],"occurrences":[5],"restricted":[7],"patterns":[8],"length":[10,17],"3":[11],"in":[12,31],"permutations":[13,30],"with":[14],"respect":[15],"to":[16],"and":[18,35],"cycles.":[22],"The":[23],"main":[24],"tool":[25],"is":[26],"a":[27],"bijection":[28],"between":[29],"standard":[32],"cycle":[33],"form":[34],"weighted":[36],"Motzkin":[37],"paths.":[38]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-01-15T23:16:33.117629","created_date":"2025-10-10T00:00:00"}