{"id":"https://openalex.org/W2767868283","doi":"https://doi.org/10.37236/1678","title":"Permutations Avoiding Two Patterns of Length Three","display_name":"Permutations Avoiding Two Patterns of Length Three","publication_year":2003,"publication_date":"2003-01-22","ids":{"openalex":"https://openalex.org/W2767868283","doi":"https://doi.org/10.37236/1678","mag":"2767868283"},"language":"en","primary_location":{"id":"doi:10.37236/1678","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1678","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i2r6/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":false,"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":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i2r6/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026309695","display_name":"Vincent Vatter","orcid":"https://orcid.org/0000-0001-5713-4059"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Vincent R. Vatter","raw_affiliation_strings":["Department of Mathematics Rutgers University, Piscataway, NJ 08854"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Rutgers University, Piscataway, NJ 08854","institution_ids":["https://openalex.org/I102322142"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5026309695"],"corresponding_institution_ids":["https://openalex.org/I102322142"],"apc_list":null,"apc_paid":null,"fwci":1.6558,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.82329317,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"9","issue":"2","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/T11428","display_name":"Advanced Mathematical Identities","score":0.9966999888420105,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9745000004768372,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8378833532333374},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8162569999694824},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5688373446464539},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.47846174240112305},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.450175017118454},{"id":"https://openalex.org/keywords/parity-of-a-permutation","display_name":"Parity of a permutation","score":0.4485897421836853},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.4337230920791626},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38798263669013977},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"Symmetric group","score":0.17889100313186646},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14015766978263855},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12428304553031921},{"id":"https://openalex.org/keywords/cyclic-permutation","display_name":"Cyclic permutation","score":0.07963752746582031}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8378833532333374},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8162569999694824},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5688373446464539},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.47846174240112305},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.450175017118454},{"id":"https://openalex.org/C64137656","wikidata":"https://www.wikidata.org/wiki/Q1064405","display_name":"Parity of a permutation","level":4,"score":0.4485897421836853},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.4337230920791626},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38798263669013977},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.17889100313186646},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14015766978263855},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12428304553031921},{"id":"https://openalex.org/C77670614","wikidata":"https://www.wikidata.org/wiki/Q212130","display_name":"Cyclic permutation","level":3,"score":0.07963752746582031},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/1678","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1678","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i2r6/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":false,"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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.10.2953","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.2953","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_9/PostScriptfiles/v9i2r6.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.124.6201","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.124.6201","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.rutgers.edu/~vatter/publications/2len3/2len3.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.3.9410","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.9410","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_9/PDF/v9i2r6.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1678","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1678","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i2r6/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":false,"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":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2767868283.pdf","grobid_xml":"https://content.openalex.org/works/W2767868283.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1489169640","https://openalex.org/W1496524398","https://openalex.org/W1543984829","https://openalex.org/W1859552527","https://openalex.org/W1951019832","https://openalex.org/W2024633196","https://openalex.org/W2049892402","https://openalex.org/W2057808121","https://openalex.org/W2067239301","https://openalex.org/W2093035529","https://openalex.org/W2094024750","https://openalex.org/W2129036921","https://openalex.org/W2165766451","https://openalex.org/W2752061190","https://openalex.org/W2752853835","https://openalex.org/W2914427938","https://openalex.org/W2951787332","https://openalex.org/W2963194896","https://openalex.org/W4212838771","https://openalex.org/W4235551663","https://openalex.org/W6605729572","https://openalex.org/W6607530787","https://openalex.org/W6631235645","https://openalex.org/W6989982117","https://openalex.org/W6998509810"],"related_works":["https://openalex.org/W2952598754","https://openalex.org/W2143566611","https://openalex.org/W2953259888","https://openalex.org/W2964309395","https://openalex.org/W2950043401","https://openalex.org/W2506973052","https://openalex.org/W2952804671","https://openalex.org/W937918267","https://openalex.org/W1715361633","https://openalex.org/W2140809923"],"abstract_inverted_index":{"We":[0,17,35],"study":[1],"permutations":[2,25,46,69],"that":[3,70],"avoid":[4,71],"two":[5,72],"distinct":[6,73],"patterns":[7,74,81],"of":[8,15,32,44,56,75,85],"length":[9,76],"three":[10,77],"and":[11,52,78],"any":[12],"additional":[13],"set":[14],"patterns.":[16],"begin":[18],"by":[19,49],"showing":[20],"how":[21,62],"to":[22,63,67],"enumerate":[23],"these":[24,65],"using":[26],"generating":[27],"trees,":[28],"generalizing":[29],"the":[30,42],"work":[31],"Mansour":[33],"[13].":[34],"then":[36],"find":[37],"sufficient":[38],"conditions":[39],"for":[40],"when":[41],"number":[43,84],"such":[45],"is":[47],"given":[48],"a":[50,54,82],"polynomial":[51],"answer":[53],"question":[55],"Egge":[57],"[6].":[58],"Afterwards,":[59],"we":[60],"show":[61],"use":[64],"computations":[66],"count":[68],"contain":[79],"other":[80],"prescribed":[83],"times.":[86]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}