{"id":"https://openalex.org/W1496896096","doi":"https://doi.org/10.37236/1344","title":"Permutations which are the union of an increasing and a decreasing subsequence","display_name":"Permutations which are the union of an increasing and a decreasing subsequence","publication_year":1998,"publication_date":"1998-01-10","ids":{"openalex":"https://openalex.org/W1496896096","doi":"https://doi.org/10.37236/1344","mag":"1496896096"},"language":"en","primary_location":{"id":"doi:10.37236/1344","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1344","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v5i1r6/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/v5i1r6/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074805691","display_name":"M. D. Atkinson","orcid":"https://orcid.org/0000-0003-4237-3588"},"institutions":[{"id":"https://openalex.org/I16835326","display_name":"University of St Andrews","ror":"https://ror.org/02wn5qz54","country_code":"GB","type":"education","lineage":["https://openalex.org/I16835326"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"M. D. Atkinson","raw_affiliation_strings":["School of Mathematical and Computational Sciences North Haugh, St Andrews, Fife KY16 9SS, UK"],"affiliations":[{"raw_affiliation_string":"School of Mathematical and Computational Sciences North Haugh, St Andrews, Fife KY16 9SS, UK","institution_ids":["https://openalex.org/I16835326"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5074805691"],"corresponding_institution_ids":["https://openalex.org/I16835326"],"apc_list":null,"apc_paid":null,"fwci":0.5228,"has_fulltext":true,"cited_by_count":43,"citation_normalized_percentile":{"value":0.63327561,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"5","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9987999796867371,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9987999796867371,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9983000159263611,"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":0.9973000288009644,"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/subsequence","display_name":"Subsequence","score":0.906474232673645},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8635914921760559},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8330951929092407},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.7237672805786133},{"id":"https://openalex.org/keywords/longest-increasing-subsequence","display_name":"Longest increasing subsequence","score":0.717735230922699},{"id":"https://openalex.org/keywords/longest-common-subsequence-problem","display_name":"Longest common subsequence problem","score":0.4771946370601654},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39351338148117065},{"id":"https://openalex.org/keywords/genetics","display_name":"Genetics","score":0.0561775267124176}],"concepts":[{"id":"https://openalex.org/C137877099","wikidata":"https://www.wikidata.org/wiki/Q1332977","display_name":"Subsequence","level":3,"score":0.906474232673645},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8635914921760559},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8330951929092407},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.7237672805786133},{"id":"https://openalex.org/C170006305","wikidata":"https://www.wikidata.org/wiki/Q4183855","display_name":"Longest increasing subsequence","level":4,"score":0.717735230922699},{"id":"https://openalex.org/C120098539","wikidata":"https://www.wikidata.org/wiki/Q141001","display_name":"Longest common subsequence problem","level":2,"score":0.4771946370601654},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39351338148117065},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0561775267124176},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/1344","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1344","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v5i1r6/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"}],"best_oa_location":{"id":"doi:10.37236/1344","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1344","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v5i1r6/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":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1496896096.pdf","grobid_xml":"https://content.openalex.org/works/W1496896096.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W196429902","https://openalex.org/W1600795850","https://openalex.org/W2006075137","https://openalex.org/W2912910446","https://openalex.org/W3198160809"],"related_works":["https://openalex.org/W1540010783","https://openalex.org/W3022573534","https://openalex.org/W1746697883","https://openalex.org/W4225868058","https://openalex.org/W4389489786","https://openalex.org/W2152064395","https://openalex.org/W4289596129","https://openalex.org/W2969919693","https://openalex.org/W3083981518","https://openalex.org/W3094761360"],"abstract_inverted_index":{"It":[0],"is":[1],"shown":[2],"that":[3],"there":[4],"are":[5,11],"${2n\\choose":[6],"n}-\\sum_{m=0}^{n-1}2^{n-m-1}{2m\\choose":[7],"m}$":[8],"permutations":[9],"which":[10],"the":[12],"union":[13],"of":[14],"an":[15],"increasing":[16],"sequence":[17],"and":[18],"a":[19],"decreasing":[20],"sequence.":[21]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}