{"id":"https://openalex.org/W3035223302","doi":"https://doi.org/10.37236/9642","title":"Sorting with Pattern-Avoiding Stacks: The 132-Machine","display_name":"Sorting with Pattern-Avoiding Stacks: The 132-Machine","publication_year":2020,"publication_date":"2020-08-21","ids":{"openalex":"https://openalex.org/W3035223302","doi":"https://doi.org/10.37236/9642","mag":"3035223302"},"language":"en","primary_location":{"id":"doi:10.37236/9642","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9642","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p32/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p32/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015643450","display_name":"Giulio Cerbai","orcid":"https://orcid.org/0000-0002-7020-4020"},"institutions":[{"id":"https://openalex.org/I4210112122","display_name":"Florence (Netherlands)","ror":"https://ror.org/021qg3d64","country_code":"NL","type":"company","lineage":["https://openalex.org/I4210112122"]},{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT","NL"],"is_corresponding":false,"raw_author_name":"Giulio Cerbai","raw_affiliation_strings":["University of Firenze","Univ of Florence"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Firenze","institution_ids":["https://openalex.org/I45084792"]},{"raw_affiliation_string":"Univ of Florence","institution_ids":["https://openalex.org/I4210112122"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034916191","display_name":"Anders Claesson","orcid":"https://orcid.org/0000-0001-5797-8673"},"institutions":[{"id":"https://openalex.org/I165368041","display_name":"University of Iceland","ror":"https://ror.org/01db6h964","country_code":"IS","type":"education","lineage":["https://openalex.org/I165368041"]}],"countries":["IS"],"is_corresponding":false,"raw_author_name":"Anders Claesson","raw_affiliation_strings":["Science Institute, University of Iceland, Iceland","University of Iceland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Science Institute, University of Iceland, Iceland","institution_ids":["https://openalex.org/I165368041"]},{"raw_affiliation_string":"University of Iceland","institution_ids":["https://openalex.org/I165368041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017390053","display_name":"Luca Ferrari","orcid":"https://orcid.org/0000-0001-8096-6865"},"institutions":[{"id":"https://openalex.org/I4210112122","display_name":"Florence (Netherlands)","ror":"https://ror.org/021qg3d64","country_code":"NL","type":"company","lineage":["https://openalex.org/I4210112122"]},{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT","NL"],"is_corresponding":false,"raw_author_name":"Luca Ferrari","raw_affiliation_strings":["University of Firenze","Univ of Florence"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Firenze","institution_ids":["https://openalex.org/I45084792"]},{"raw_affiliation_string":"Univ of Florence","institution_ids":["https://openalex.org/I4210112122"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022742638","display_name":"Einar Steingr\u0131\u0301msson","orcid":"https://orcid.org/0000-0003-3965-7280"},"institutions":[{"id":"https://openalex.org/I181647926","display_name":"University of Strathclyde","ror":"https://ror.org/00n3w3b69","country_code":"GB","type":"education","lineage":["https://openalex.org/I181647926"]},{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["GB","IT"],"is_corresponding":false,"raw_author_name":"Einar Steingr\u00edmsson","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Strathclyde, Glasgow, Scotland","University of Florence"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Strathclyde, Glasgow, Scotland","institution_ids":["https://openalex.org/I181647926"]},{"raw_affiliation_string":"University of Florence","institution_ids":["https://openalex.org/I45084792"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5476,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.6056598,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"27","issue":"3","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/T11567","display_name":"semigroups and automata theory","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9984999895095825,"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/enumeration","display_name":"Enumeration","score":0.8716945648193359},{"id":"https://openalex.org/keywords/sorting","display_name":"Sorting","score":0.7436546087265015},{"id":"https://openalex.org/keywords/stack","display_name":"Stack (abstract data type)","score":0.7363600730895996},{"id":"https://openalex.org/keywords/sort","display_name":"sort","score":0.7356555461883545},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.7120221853256226},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.664232611656189},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5884480476379395},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5884326100349426},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4785500168800354},{"id":"https://openalex.org/keywords/pattern-matching","display_name":"Pattern matching","score":0.43729591369628906},{"id":"https://openalex.org/keywords/encode","display_name":"ENCODE","score":0.4290415346622467},{"id":"https://openalex.org/keywords/topological-sorting","display_name":"Topological sorting","score":0.41454583406448364},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3810306191444397},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3714015483856201},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2964664697647095},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.16642627120018005},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.14262443780899048},{"id":"https://openalex.org/keywords/information-retrieval","display_name":"Information retrieval","score":0.06428447365760803}],"concepts":[{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.8716945648193359},{"id":"https://openalex.org/C111696304","wikidata":"https://www.wikidata.org/wiki/Q2303697","display_name":"Sorting","level":2,"score":0.7436546087265015},{"id":"https://openalex.org/C9395851","wikidata":"https://www.wikidata.org/wiki/Q177929","display_name":"Stack (abstract data type)","level":2,"score":0.7363600730895996},{"id":"https://openalex.org/C88548561","wikidata":"https://www.wikidata.org/wiki/Q347599","display_name":"sort","level":2,"score":0.7356555461883545},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.7120221853256226},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.664232611656189},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5884480476379395},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5884326100349426},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4785500168800354},{"id":"https://openalex.org/C68859911","wikidata":"https://www.wikidata.org/wiki/Q1503724","display_name":"Pattern matching","level":2,"score":0.43729591369628906},{"id":"https://openalex.org/C66746571","wikidata":"https://www.wikidata.org/wiki/Q1134833","display_name":"ENCODE","level":3,"score":0.4290415346622467},{"id":"https://openalex.org/C176032523","wikidata":"https://www.wikidata.org/wiki/Q753127","display_name":"Topological sorting","level":3,"score":0.41454583406448364},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3810306191444397},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3714015483856201},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2964664697647095},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.16642627120018005},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.14262443780899048},{"id":"https://openalex.org/C23123220","wikidata":"https://www.wikidata.org/wiki/Q816826","display_name":"Information retrieval","level":1,"score":0.06428447365760803},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/9642","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9642","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p32/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2006.05692","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.05692","pdf_url":"https://arxiv.org/pdf/2006.05692","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:strathprints.strath.ac.uk:74350","is_oa":true,"landing_page_url":"https://strathprints.strath.ac.uk/view/author/780992.html>","pdf_url":"https://strathprints.strath.ac.uk/74350/1/Cerbai_etal_EJC_2020_Sorting_with_pattern_avoiding_stacks_the_132.pdf","source":{"id":"https://openalex.org/S4306402226","display_name":"Strathprints: The University of Strathclyde institutional repository (University of Strathclyde)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I181647926","host_organization_name":"University of Strathclyde","host_organization_lineage":["https://openalex.org/I181647926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"mag:3035223302","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2006.05692.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2006.05692","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2006.05692","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.37236/9642","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9642","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p32/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/G1136033885","display_name":null,"funder_award_id":"INdAM-GNCS 2020","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G3093964658","display_name":null,"funder_award_id":"2016-06596","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"},{"id":"https://openalex.org/G5829525057","display_name":null,"funder_award_id":"GNCS 2020 project","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G6473949287","display_name":null,"funder_award_id":"GNCS 2020","funder_id":"https://openalex.org/F4320334079","funder_display_name":"Gruppo Nazionale per il Calcolo Scientifico"}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320319993","display_name":"Leverhulme Trust","ror":"https://ror.org/012mzw131"},{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"},{"id":"https://openalex.org/F4320334079","display_name":"Gruppo Nazionale per il Calcolo Scientifico","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3035223302.pdf","grobid_xml":"https://content.openalex.org/works/W3035223302.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1530744624","https://openalex.org/W1893850285","https://openalex.org/W1941271855","https://openalex.org/W1978985258","https://openalex.org/W2014724230","https://openalex.org/W2024532720","https://openalex.org/W2063451706","https://openalex.org/W2135805766","https://openalex.org/W2173817930","https://openalex.org/W2611531305","https://openalex.org/W2697533926","https://openalex.org/W2752853835","https://openalex.org/W2963778499","https://openalex.org/W6805331278","https://openalex.org/W6819624514"],"related_works":["https://openalex.org/W3083001871","https://openalex.org/W3006907031","https://openalex.org/W1781970429","https://openalex.org/W3159962322","https://openalex.org/W34396323","https://openalex.org/W3010098092","https://openalex.org/W2952073729","https://openalex.org/W1704788265","https://openalex.org/W1579375726","https://openalex.org/W2945147107","https://openalex.org/W2980623943","https://openalex.org/W2892050462","https://openalex.org/W2992937527","https://openalex.org/W2952639400","https://openalex.org/W2890646761","https://openalex.org/W2515185299","https://openalex.org/W2733797194","https://openalex.org/W2999906390","https://openalex.org/W1542841928","https://openalex.org/W2949429561"],"abstract_inverted_index":{"This":[0],"paper":[1],"continues":[2],"the":[3,6,36,54,63,71,76,111,125],"analysis":[4],"of":[5,21,38,56,70,113,116],"pattern-avoiding":[7,117],"sorting":[8],"machines":[9],"recently":[10],"introduced":[11,127],"by":[12,75],"Cerbai,":[13],"Claesson":[14],"and":[15,52,97,121],"Ferrari":[16],"(2020).":[17],"These":[18],"devices":[19],"consist":[20],"two":[22],"stacks,":[23],"through":[24],"which":[25],"a":[26,46],"permutation":[27],"is":[28,66],"passed":[29],"in":[30],"order":[31],"to":[32,132],"sort":[33],"it,":[34],"where":[35],"content":[37],"each":[39],"stack":[40,65],"must":[41],"at":[42],"all":[43],"times":[44],"avoid":[45],"certain":[47],"pattern.":[48],"Here":[49],"we":[50,83,122],"characterize":[51],"enumerate":[53],"set":[55,103],"permutations":[57],"that":[58,81,124],"can":[59,128],"be":[60,129],"sorted":[61],"when":[62],"first":[64],"$132$-avoiding,":[67],"solving":[68],"one":[69],"open":[72],"problems":[73],"proposed":[74],"above":[77],"mentioned":[78],"authors.":[79],"To":[80],"end":[82],"present":[84],"several":[85],"connections":[86],"with":[87],"other":[88],"well":[89],"known":[90],"combinatorial":[91],"objects,":[92],"such":[93],"as":[94],"lattice":[95],"paths":[96],"restricted":[98,118],"growth":[99,119],"functions":[100,120],"(which":[101],"encode":[102],"partitions).":[104],"We":[105],"also":[106],"provide":[107],"new":[108],"proofs":[109],"for":[110],"enumeration":[112],"some":[114],"sets":[115],"expect":[123],"tools":[126],"fruitfully":[130],"employed":[131],"get":[133],"further":[134],"similar":[135],"results.":[136]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}