{"id":"https://openalex.org/W2110385536","doi":"https://doi.org/10.37236/610","title":"The Quantifier Semigroup for Bipartite Graphs","display_name":"The Quantifier Semigroup for Bipartite Graphs","publication_year":2011,"publication_date":"2011-05-30","ids":{"openalex":"https://openalex.org/W2110385536","doi":"https://doi.org/10.37236/610","mag":"2110385536"},"language":"en","primary_location":{"id":"doi:10.37236/610","is_oa":true,"landing_page_url":"https://doi.org/10.37236/610","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p123/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/v18i1p123/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065859226","display_name":"Leonard J. Schulman","orcid":"https://orcid.org/0000-0001-9901-2797"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Leonard J. Schulman","raw_affiliation_strings":["Caltech, Pasadena, CA 91125","California  Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Caltech, Pasadena, CA 91125","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"California  Institute of Technology","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5065859226"],"corresponding_institution_ids":["https://openalex.org/I122411786"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15574761,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"18","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9997000098228455,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9970999956130981,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9769999980926514,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8956362009048462},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.8540360927581787},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7327154874801636},{"id":"https://openalex.org/keywords/quantifier","display_name":"Quantifier (linguistics)","score":0.6735052466392517},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6602622270584106},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.6136302351951599},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5728077292442322},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5358086824417114},{"id":"https://openalex.org/keywords/complete-bipartite-graph","display_name":"Complete bipartite graph","score":0.5182647705078125},{"id":"https://openalex.org/keywords/quantifier-elimination","display_name":"Quantifier elimination","score":0.43726611137390137},{"id":"https://openalex.org/keywords/robertson\u2013seymour-theorem","display_name":"Robertson\u2013Seymour theorem","score":0.43675318360328674},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.19444355368614197},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.15590310096740723},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.052825093269348145}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8956362009048462},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.8540360927581787},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7327154874801636},{"id":"https://openalex.org/C2778523021","wikidata":"https://www.wikidata.org/wiki/Q5532504","display_name":"Quantifier (linguistics)","level":2,"score":0.6735052466392517},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6602622270584106},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.6136302351951599},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5728077292442322},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5358086824417114},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.5182647705078125},{"id":"https://openalex.org/C32278780","wikidata":"https://www.wikidata.org/wiki/Q1849020","display_name":"Quantifier elimination","level":2,"score":0.43726611137390137},{"id":"https://openalex.org/C173644813","wikidata":"https://www.wikidata.org/wiki/Q3527155","display_name":"Robertson\u2013Seymour theorem","level":5,"score":0.43675318360328674},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.19444355368614197},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.15590310096740723},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.052825093269348145},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/610","is_oa":true,"landing_page_url":"https://doi.org/10.37236/610","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p123/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"},{"id":"pmh:oai:authors.library.caltech.edu:24053","is_oa":false,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20110620-085724958","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.372.5898","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.372.5898","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/ojs/index.php/eljc/article/viewFile/v18i1p123/pdf/","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/610","is_oa":true,"landing_page_url":"https://doi.org/10.37236/610","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p123/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/G2118814157","display_name":"Algorithms for Data Analysis","funder_award_id":"0515342","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G303052165","display_name":"Collaborative Research:  EMT/QIS:  Quantum Algorithms and Post-Quantum Cryptography","funder_award_id":"0829909","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6441408578","display_name":"ITR: Information Dynamics for Networked Feedback Systems","funder_award_id":"0326554","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"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2110385536.pdf","grobid_xml":"https://content.openalex.org/works/W2110385536.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W976211528","https://openalex.org/W1597075609","https://openalex.org/W1968871074","https://openalex.org/W1978188779","https://openalex.org/W1997318331","https://openalex.org/W2014027305","https://openalex.org/W2086037765","https://openalex.org/W2318541840","https://openalex.org/W2914659449","https://openalex.org/W2949176902","https://openalex.org/W4384817650"],"related_works":["https://openalex.org/W4214737172","https://openalex.org/W3012938552","https://openalex.org/W2324712051","https://openalex.org/W4287825236","https://openalex.org/W1239946963","https://openalex.org/W71729059","https://openalex.org/W1524103539","https://openalex.org/W3216731410","https://openalex.org/W1973527399","https://openalex.org/W2798639752"],"abstract_inverted_index":{"In":[0],"a":[1,32,52],"bipartite":[2],"graph":[3,18],"there":[4],"are":[5,45],"two":[6],"widely":[7],"encountered":[8],"monotone":[9],"mappings":[10,50],"from":[11],"subsets":[12,20],"of":[13,16,21,61],"one":[14,25],"side":[15],"the":[17,22,28,35,38,41,47],"to":[19,27,40],"other":[23,39],"side:":[24],"corresponds":[26],"quantifier":[29,42],"\"there":[30],"exists":[31],"neighbor":[33],"in":[34,46,59],"subset\"":[36],"and":[37],"\"all":[43],"neighbors":[44],"subset.\"":[48],"These":[49],"generate":[51],"partially":[53],"ordered":[54],"semigroup":[55],"which":[56],"we":[57],"characterize":[58],"terms":[60],"\"run-unimodal\"":[62],"words.":[63]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}