{"id":"https://openalex.org/W2171119954","doi":"https://doi.org/10.1155/s0161171204304114","title":"Counting occurrences of 132 in an even permutation","display_name":"Counting occurrences of 132 in an even permutation","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2171119954","doi":"https://doi.org/10.1155/s0161171204304114","mag":"2171119954"},"language":"en","primary_location":{"id":"doi:10.1155/s0161171204304114","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s0161171204304114","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2004/814616.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2004/814616.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024416044","display_name":"Toufik Mansour","orcid":"https://orcid.org/0000-0001-8028-2391"},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Toufik Mansour","raw_affiliation_strings":["Department of Mathematics, Chalmers University of Technology, G\u00f6teborg 41296, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Chalmers University of Technology, G\u00f6teborg 41296, Sweden","institution_ids":["https://openalex.org/I66862912"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5024416044"],"corresponding_institution_ids":["https://openalex.org/I66862912"],"apc_list":{"value":1050,"currency":"USD","value_usd":1050},"apc_paid":{"value":1050,"currency":"USD","value_usd":1050},"fwci":2.9765,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.91057338,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"2004","issue":"25","first_page":"1329","last_page":"1341"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9991999864578247,"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":0.9991999864578247,"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/T11130","display_name":"Coding theory and cryptography","score":0.996999979019165,"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/T11269","display_name":"Algorithms and Data Compression","score":0.996399998664856,"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/mathematics","display_name":"Mathematics","score":0.8658307790756226},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.8174119591712952},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.777064859867096},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.6999198198318481},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5462847948074341},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4000178575515747}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8658307790756226},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.8174119591712952},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.777064859867096},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.6999198198318481},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5462847948074341},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4000178575515747},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/s0161171204304114","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s0161171204304114","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2004/814616.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:88a62c6bd993423e8303c327c36c6c64","is_oa":false,"landing_page_url":"https://doaj.org/article/88a62c6bd993423e8303c327c36c6c64","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2004, Iss 25, Pp 1329-1341 (2004)","raw_type":"article"},{"id":"pmh:oai:doaj.org/article:fd4ff12ab6c14b22886000800099a8c1","is_oa":true,"landing_page_url":"https://doaj.org/article/fd4ff12ab6c14b22886000800099a8c1","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2004, Iss 25, Pp 1329-1341 (2004)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/s0161171204304114","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s0161171204304114","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2004/814616.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2171119954.pdf","grobid_xml":"https://content.openalex.org/works/W2171119954.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1607320696","https://openalex.org/W1662894401","https://openalex.org/W1678540464","https://openalex.org/W1998726440","https://openalex.org/W2003628938","https://openalex.org/W2014559994","https://openalex.org/W2021480278","https://openalex.org/W2029340507","https://openalex.org/W2038250522","https://openalex.org/W2047160913","https://openalex.org/W2062437114","https://openalex.org/W2074370694","https://openalex.org/W2088683615","https://openalex.org/W2094024750","https://openalex.org/W2167602228","https://openalex.org/W2468454950","https://openalex.org/W2752061190","https://openalex.org/W2752853835","https://openalex.org/W2912910446","https://openalex.org/W2914427938","https://openalex.org/W2952402095","https://openalex.org/W3198160809","https://openalex.org/W4212838771","https://openalex.org/W6600402863","https://openalex.org/W6605729572","https://openalex.org/W6606511383","https://openalex.org/W6607530787","https://openalex.org/W6630378981"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2950949433","https://openalex.org/W2071280507","https://openalex.org/W2163837436","https://openalex.org/W4301731691","https://openalex.org/W2000985996","https://openalex.org/W4386833582","https://openalex.org/W1603880452","https://openalex.org/W2997844930","https://openalex.org/W3024985242"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,6],"generating":[3],"function":[4,32],"for":[5,33],"number":[7],"of":[8,22,42],"even":[9],"(or":[10],"odd)":[11],"permutations":[12,44],"on":[13],"n":[14],"letters":[15],"containing":[16],"exactly":[17],"r":[18,36,48],"\u2265":[19],"0":[20],"occurrences":[21],"a":[23,34,39],"132":[24],"pattern.":[25],"It":[26],"is":[27],"shown":[28],"that":[29],"finding":[30],"this":[31],"given":[35],"amounts":[37],"to":[38],"routine":[40],"check":[41],"all":[43],"in":[45],"𝔖":[46],"2":[47],".":[49]},"counts_by_year":[],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2016-06-24T00:00:00"}