{"id":"https://openalex.org/W2108027351","doi":"https://doi.org/10.37236/2472","title":"On 021-Avoiding Ascent Sequences","display_name":"On 021-Avoiding Ascent Sequences","publication_year":2013,"publication_date":"2013-03-31","ids":{"openalex":"https://openalex.org/W2108027351","doi":"https://doi.org/10.37236/2472","mag":"2108027351"},"language":"en","primary_location":{"id":"doi:10.37236/2472","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2472","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i1p76/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/v20i1p76/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074795333","display_name":"William Y. C. Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"William Y.C. Chen","raw_affiliation_strings":["Center for Combinatorics\r\nNankai University","Center for Combinatorics#R##N#Nankai University"],"affiliations":[{"raw_affiliation_string":"Center for Combinatorics\r\nNankai University","institution_ids":["https://openalex.org/I205237279"]},{"raw_affiliation_string":"Center for Combinatorics#R##N#Nankai University","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050216505","display_name":"Alvin Y. L. Dai","orcid":null},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Alvin Y.L. Dai","raw_affiliation_strings":["Center for Combinatorics\r\nNankai University","Center for Combinatorics#R##N#Nankai University"],"affiliations":[{"raw_affiliation_string":"Center for Combinatorics\r\nNankai University","institution_ids":["https://openalex.org/I205237279"]},{"raw_affiliation_string":"Center for Combinatorics#R##N#Nankai University","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036938797","display_name":"Theodore Dokos","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Theodore Dokos","raw_affiliation_strings":["Department of Mathematics\r\nUniversity of California","Department of Mathematics#R##N#University of California"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics\r\nUniversity of California","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics#R##N#University of California","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008149778","display_name":"Tim Dwyer","orcid":"https://orcid.org/0000-0002-9076-9571"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tim Dwyer","raw_affiliation_strings":["Department of Mathematics\r\nDartmouth College","Department of Mathematics#R##N#Dartmouth College"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics\r\nDartmouth College","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics#R##N#Dartmouth College","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070369805","display_name":"Bruce E. Sagan","orcid":"https://orcid.org/0000-0001-7700-6353"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bruce E. Sagan","raw_affiliation_strings":["Department of Mathematics\r\nState University","Department of Mathematics#R##N#State University"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics\r\nState University","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics#R##N#State University","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5074795333"],"corresponding_institution_ids":["https://openalex.org/I205237279"],"apc_list":null,"apc_paid":null,"fwci":2.4888,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.9069838,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"20","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9991999864578247,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9988999962806702,"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/T11567","display_name":"semigroups and automata theory","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/equidistributed-sequence","display_name":"Equidistributed sequence","score":0.9392040967941284},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8751586079597473},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.7947699427604675},{"id":"https://openalex.org/keywords/bijection-injection-and-surjection","display_name":"Bijection, injection and surjection","score":0.775025486946106},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6986806988716125},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6876220107078552},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5649124979972839},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.49587783217430115}],"concepts":[{"id":"https://openalex.org/C50742451","wikidata":"https://www.wikidata.org/wiki/Q1530388","display_name":"Equidistributed sequence","level":2,"score":0.9392040967941284},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8751586079597473},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.7947699427604675},{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.775025486946106},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6986806988716125},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6876220107078552},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5649124979972839},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.49587783217430115},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/2472","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2472","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i1p76/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:10.37236/2472","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2472","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i1p76/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":[{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3151526626","display_name":null,"funder_award_id":"PCSIRT","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4020255992","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2108027351.pdf","grobid_xml":"https://content.openalex.org/works/W2108027351.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1491236022","https://openalex.org/W1866129717","https://openalex.org/W1893850285","https://openalex.org/W1984841421","https://openalex.org/W2048655899","https://openalex.org/W2090855500","https://openalex.org/W2121947368","https://openalex.org/W2950489658","https://openalex.org/W2963222194","https://openalex.org/W4212838771","https://openalex.org/W4237930722"],"related_works":["https://openalex.org/W2952259524","https://openalex.org/W2160566290","https://openalex.org/W2806276129","https://openalex.org/W4299611798","https://openalex.org/W2963449060","https://openalex.org/W2021895108","https://openalex.org/W4213409680","https://openalex.org/W2949947309","https://openalex.org/W2153752510","https://openalex.org/W2602388795"],"abstract_inverted_index":{"Ascent":[0],"sequences":[1,64,72],"were":[2],"introduced":[3],"by":[4,138],"Bousquet-M\u00e9lou,":[5],"Claesson,":[6],"Dukes":[7],"and":[8,32,65,93,124],"Kitaev":[9],"in":[10,50,87],"their":[11],"study":[12],"of":[13,19,48,62,71,84],"$(\\bf{2+2})$-free":[14],"posets.":[15],"An":[16],"ascent":[17,99],"sequence":[18,26,52],"length":[20],"$n$":[21],"is":[22,45,120,129],"a":[23,74,140],"nonnegative":[24],"integer":[25],"$x=x_{1}x_{2}\\ldots":[27],"x_{n}$":[28],"such":[29,63],"that":[30,97,113],"$x_{1}=0$":[31],"$x_{i}\\leq":[33],"{\\rm":[34,118],"asc}(x_{1}x_{2}\\ldots":[35,43],"x_{i-1})+1$":[36],"for":[37,59,68],"all":[38],"$1&lt;i\\leq":[39],"n$,":[40],"where":[41,126],"${\\rm":[42,127],"x_{i-1})$":[44],"the":[46,51,60,69,82,88,98,102,114,130],"number":[47],"ascents":[49],"$x_{1}x_{2}\\ldots":[53],"x_{i-1}$.":[54],"We":[55,134],"let":[56,79],"$\\mathcal{A}_n$":[57],"stand":[58],"set":[61,83],"use":[66],"$\\mathcal{A}_n(p)$":[67],"subset":[70],"avoiding":[73],"pattern":[75],"$p$.":[76],"Similarly,":[77],"we":[78],"$S_{n}(\\tau)$":[80],"be":[81],"$\\tau$-avoiding":[85],"permutations":[86],"symmetric":[89],"group":[90],"$S_{n}$.":[91],"Duncan":[92],"Steingr\u00edmsson":[94],"have":[95],"shown":[96],"statistic":[100],"has":[101],"same":[103],"distribution":[104],"over":[105,108,122],"$\\mathcal{A}_n(021)$":[106,123],"as":[107],"$S_n(132)$.":[109],"Furthermore,":[110],"they":[111],"conjectured":[112],"pair":[115],"$({\\rm":[116],"asc},":[117],"rmin})$":[119],"equidistributed":[121],"$S_n(132)$":[125],"rmin}$":[128],"right-to-left":[131],"minima":[132],"statistic.":[133],"prove":[135],"this":[136],"conjecture":[137],"constructing":[139],"bistatistic-preserving":[141],"bijection.":[142]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}
