{"id":"https://openalex.org/W1551489578","doi":"https://doi.org/10.37236/225","title":"Counting $1324$, $4231$-Avoiding Permutations","display_name":"Counting $1324$, $4231$-Avoiding Permutations","publication_year":2009,"publication_date":"2009-11-13","ids":{"openalex":"https://openalex.org/W1551489578","doi":"https://doi.org/10.37236/225","mag":"1551489578"},"language":"en","primary_location":{"id":"doi:10.37236/225","is_oa":true,"landing_page_url":"https://doi.org/10.37236/225","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r136/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/v16i1r136/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001631971","display_name":"Michael Albert","orcid":"https://orcid.org/0009-0006-0659-7743"},"institutions":[{"id":"https://openalex.org/I80281795","display_name":"University of Otago","ror":"https://ror.org/01jmxt844","country_code":"NZ","type":"education","lineage":["https://openalex.org/I80281795"]}],"countries":["NZ"],"is_corresponding":true,"raw_author_name":"Michael H. Albert","raw_affiliation_strings":["Department of Computer Science University of Otago Dunedin, New Zealand","University of Otago"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science University of Otago Dunedin, New Zealand","institution_ids":["https://openalex.org/I80281795"]},{"raw_affiliation_string":"University of Otago","institution_ids":["https://openalex.org/I80281795"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074805691","display_name":"M. D. Atkinson","orcid":"https://orcid.org/0000-0003-4237-3588"},"institutions":[{"id":"https://openalex.org/I80281795","display_name":"University of Otago","ror":"https://ror.org/01jmxt844","country_code":"NZ","type":"education","lineage":["https://openalex.org/I80281795"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"M. D. Atkinson","raw_affiliation_strings":["Department of Computer Science University of Otago Dunedin, New Zealand","University of Otago"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science University of Otago Dunedin, New Zealand","institution_ids":["https://openalex.org/I80281795"]},{"raw_affiliation_string":"University of Otago","institution_ids":["https://openalex.org/I80281795"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026309695","display_name":"Vincent Vatter","orcid":"https://orcid.org/0000-0001-5713-4059"},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]},{"id":"https://openalex.org/I4210166639","display_name":"Dartmouth Hospital","ror":"https://ror.org/02j3qj605","country_code":"GB","type":"healthcare","lineage":["https://openalex.org/I4210166639"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Vincent Vatter","raw_affiliation_strings":["Department of Mathematics Dartmouth College Hanover, New Hampshire USA","Dartmouth College"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Dartmouth College Hanover, New Hampshire USA","institution_ids":["https://openalex.org/I107672454"]},{"raw_affiliation_string":"Dartmouth College","institution_ids":["https://openalex.org/I4210166639","https://openalex.org/I107672454"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5001631971"],"corresponding_institution_ids":["https://openalex.org/I80281795"],"apc_list":null,"apc_paid":null,"fwci":0.96,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.66547021,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"16","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":0.9997000098228455,"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":0.9997000098228455,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.993399977684021,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.8999558091163635},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8263580799102783},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.683010995388031},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.4202038645744324},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3420167565345764}],"concepts":[{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.8999558091163635},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8263580799102783},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.683010995388031},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.4202038645744324},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3420167565345764},{"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":1,"locations":[{"id":"doi:10.37236/225","is_oa":true,"landing_page_url":"https://doi.org/10.37236/225","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r136/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:10.37236/225","is_oa":true,"landing_page_url":"https://doi.org/10.37236/225","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r136/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":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1551489578.pdf","grobid_xml":"https://content.openalex.org/works/W1551489578.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1583030682","https://openalex.org/W1621837664","https://openalex.org/W1706877037","https://openalex.org/W1981803420","https://openalex.org/W2011790063","https://openalex.org/W2024633196","https://openalex.org/W2041026622","https://openalex.org/W2045267534","https://openalex.org/W2056117952","https://openalex.org/W2129036921","https://openalex.org/W2143566611","https://openalex.org/W2143645603","https://openalex.org/W3103273172","https://openalex.org/W4235551663"],"related_works":["https://openalex.org/W108845024","https://openalex.org/W4300125793","https://openalex.org/W2578985712","https://openalex.org/W2406961474","https://openalex.org/W2013740965","https://openalex.org/W588267724","https://openalex.org/W4297743441","https://openalex.org/W2952598754","https://openalex.org/W2143566611","https://openalex.org/W2953259888"],"abstract_inverted_index":{"A":[0],"complete":[1],"structural":[2],"description":[3],"and":[4,14],"enumeration":[5],"is":[6],"found":[7],"for":[8],"permutations":[9],"that":[10],"avoid":[11],"both":[12],"$1324$":[13],"$4231$.":[15]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}