{"id":"https://openalex.org/W2168038618","doi":"https://doi.org/10.37236/2442","title":"The Enumeration of Three Pattern Classes using Monotone Grid Classes","display_name":"The Enumeration of Three Pattern Classes using Monotone Grid Classes","publication_year":2012,"publication_date":"2012-08-16","ids":{"openalex":"https://openalex.org/W2168038618","doi":"https://doi.org/10.37236/2442","mag":"2168038618"},"language":"en","primary_location":{"id":"doi:10.37236/2442","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2442","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i3p20/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/v19i3p20/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030851924","display_name":"Michael H. Albert","orcid":"https://orcid.org/0000-0001-9143-3263"},"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 Albert","raw_affiliation_strings":["University of Otago"],"affiliations":[{"raw_affiliation_string":"University of Otago","institution_ids":["https://openalex.org/I80281795"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103972047","display_name":"Mike Atkinson","orcid":null},"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":"Mike Atkinson","raw_affiliation_strings":["University of Otago"],"affiliations":[{"raw_affiliation_string":"University of Otago","institution_ids":["https://openalex.org/I80281795"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000016207","display_name":"Robert Brignall","orcid":"https://orcid.org/0000-0002-2769-4853"},"institutions":[{"id":"https://openalex.org/I204136569","display_name":"The Open University","ror":"https://ror.org/05mzfcs16","country_code":"GB","type":"education","lineage":["https://openalex.org/I204136569"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Robert Brignall","raw_affiliation_strings":["The Open University"],"affiliations":[{"raw_affiliation_string":"The Open University","institution_ids":["https://openalex.org/I204136569"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5030851924"],"corresponding_institution_ids":["https://openalex.org/I80281795"],"apc_list":null,"apc_paid":null,"fwci":2.9538,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.91629431,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"19","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":0.9995999932289124,"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":0.9995999932289124,"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":0.9991000294685364,"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":0.9975000023841858,"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":0.8982994556427002},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.8539360761642456},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7403773069381714},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.636307418346405},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6058359146118164},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5216237306594849},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.46034669876098633},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40664130449295044},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20545777678489685}],"concepts":[{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.8982994556427002},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.8539360761642456},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7403773069381714},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.636307418346405},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6058359146118164},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5216237306594849},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.46034669876098633},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40664130449295044},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20545777678489685},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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":1,"locations":[{"id":"doi:10.37236/2442","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2442","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i3p20/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:10.37236/2442","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2442","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i3p20/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/W2168038618.pdf","grobid_xml":"https://content.openalex.org/works/W2168038618.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1574446493","https://openalex.org/W1583030682","https://openalex.org/W1626703745","https://openalex.org/W1706877037","https://openalex.org/W1981803420","https://openalex.org/W1997435682","https://openalex.org/W2005287322","https://openalex.org/W2011790063","https://openalex.org/W2024633196","https://openalex.org/W2056117952","https://openalex.org/W2092807942","https://openalex.org/W2126209209","https://openalex.org/W2129036921","https://openalex.org/W2752853835","https://openalex.org/W2752908210","https://openalex.org/W2914427938","https://openalex.org/W2949176902","https://openalex.org/W2951840794","https://openalex.org/W2994155334","https://openalex.org/W4212838771"],"related_works":["https://openalex.org/W108845024","https://openalex.org/W4300125793","https://openalex.org/W2578985712","https://openalex.org/W2406961474","https://openalex.org/W2143566611","https://openalex.org/W2013740965","https://openalex.org/W588267724","https://openalex.org/W4297743441","https://openalex.org/W2952598754","https://openalex.org/W2152772468"],"abstract_inverted_index":{"The":[0],"structure":[1],"of":[2,11,26,42],"the":[3,9,24,32,51],"three":[4],"pattern":[5],"classes":[6,36,58],"defined":[7],"by":[8],"sets":[10],"forbidden":[12],"permutations":[13,33],"$\\{2143,":[14,16],"4321\\}$,":[15],"4312\\}$":[17,20],"and":[18,45],"$\\{1324,":[19],"is":[21],"determined":[22],"using":[23,49],"machinery":[25],"monotone":[27],"grid":[28],"classes.":[29],"This":[30],"allows":[31],"in":[34,40],"these":[35,57],"to":[37],"be":[38],"described":[39],"terms":[41],"simple":[43],"diagrams":[44],"regular":[46],"languages":[47],"and,":[48],"this,":[50],"rational":[52],"generating":[53],"functions":[54],"which":[55],"enumerate":[56],"are":[59],"determined.":[60]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}