{"id":"https://openalex.org/W2135002777","doi":"https://doi.org/10.37236/531","title":"Composition Matrices, (2+2)-Free Posets and their Specializations","display_name":"Composition Matrices, (2+2)-Free Posets and their Specializations","publication_year":2011,"publication_date":"2011-02-21","ids":{"openalex":"https://openalex.org/W2135002777","doi":"https://doi.org/10.37236/531","mag":"2135002777"},"language":"en","primary_location":{"id":"doi:10.37236/531","is_oa":true,"landing_page_url":"https://doi.org/10.37236/531","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p44/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/v18i1p44/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054414618","display_name":"Mark Dukes","orcid":"https://orcid.org/0000-0002-2779-2680"},"institutions":[{"id":"https://openalex.org/I3130035786","display_name":"University Ucinf","ror":"https://ror.org/02cs9pv18","country_code":"CL","type":"education","lineage":["https://openalex.org/I3130035786"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Mark Dukes","raw_affiliation_strings":["Computer And Information Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer And Information Sciences","institution_ids":["https://openalex.org/I3130035786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005488534","display_name":"V\u00edt Jel\u00ednek","orcid":"https://orcid.org/0000-0003-4831-4079"},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"V\u00edt Jel\u00ednek","raw_affiliation_strings":["Charles University,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Charles University,","institution_ids":["https://openalex.org/I21250087"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028851515","display_name":"Martina Kubitzke","orcid":null},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Martina Kubitzke","raw_affiliation_strings":["Univ. of Vienna#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. of Vienna#TAB#","institution_ids":["https://openalex.org/I129774422"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.3841,"has_fulltext":true,"cited_by_count":25,"citation_normalized_percentile":{"value":0.98036897,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/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/T11797","display_name":"graph theory and CDMA systems","score":0.9983000159263611,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.8628925085067749},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8279320001602173},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8225641250610352},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.7877521514892578},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5875371098518372},{"id":"https://openalex.org/keywords/composition","display_name":"Composition (language)","score":0.5292192101478577},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.4477519989013672},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4422767758369446},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.43904826045036316},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.43239128589630127},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3493254780769348},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.08388128876686096}],"concepts":[{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.8628925085067749},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8279320001602173},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8225641250610352},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.7877521514892578},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5875371098518372},{"id":"https://openalex.org/C40231798","wikidata":"https://www.wikidata.org/wiki/Q1333743","display_name":"Composition (language)","level":2,"score":0.5292192101478577},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.4477519989013672},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4422767758369446},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.43904826045036316},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.43239128589630127},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3493254780769348},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.08388128876686096},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","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},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/531","is_oa":true,"landing_page_url":"https://doi.org/10.37236/531","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p44/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:strathprints.strath.ac.uk:34523","is_oa":false,"landing_page_url":"https://strathprints.strath.ac.uk/34523/","pdf_url":null,"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"}],"best_oa_location":{"id":"doi:10.37236/531","is_oa":true,"landing_page_url":"https://doi.org/10.37236/531","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p44/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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2135002777.pdf","grobid_xml":"https://content.openalex.org/works/W2135002777.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1579213680","https://openalex.org/W1866129717","https://openalex.org/W1973597486","https://openalex.org/W2038372936","https://openalex.org/W2076847076","https://openalex.org/W2077624763","https://openalex.org/W2121947368","https://openalex.org/W2300684981","https://openalex.org/W2952552917","https://openalex.org/W3197565569","https://openalex.org/W4285719527","https://openalex.org/W4384817650","https://openalex.org/W6669693135"],"related_works":["https://openalex.org/W2054008041","https://openalex.org/W2952295216","https://openalex.org/W4299355653","https://openalex.org/W802045817","https://openalex.org/W4237490700","https://openalex.org/W3011729766","https://openalex.org/W1686955344","https://openalex.org/W2512989490","https://openalex.org/W4309131384","https://openalex.org/W2217273853"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"present":[4],"a":[5,23,45,62,76],"bijection":[6,14,24],"between":[7],"composition":[8,57,83,104],"matrices":[9,17,28],"and":[10,21,96],"($\\mathbf{2+2}$)-free":[11,41,46],"posets.":[12,42],"This":[13],"maps":[15],"partition":[16],"to":[18,39,50,52,79],"factorial":[19],"posets,":[20],"induces":[22],"from":[25],"upper":[26],"triangular":[27],"with":[29],"non-negative":[30],"entries":[31,53],"having":[32],"no":[33],"rows":[34],"or":[35],"columns":[36],"of":[37,71,75,101],"zeros":[38],"unlabeled":[40],"Chains":[43],"in":[44,54,85],"poset":[47,77],"are":[48,93],"shown":[49,67],"correspond":[51],"the":[55,69,73,81],"associated":[56,82,103],"matrix":[58,84],"whose":[59],"hooks":[60],"satisfy":[61],"simple":[63],"condition.":[64],"It":[65],"is":[66],"that":[68],"action":[70],"taking":[72],"dual":[74],"corresponds":[78],"reflecting":[80],"its":[86],"anti-diagonal.":[87],"We":[88],"further":[89],"characterize":[90],"posets":[91],"which":[92],"both":[94],"($\\mathbf{2+2}$)-":[95],"($\\mathbf{3+1}$)-free":[97],"by":[98],"certain":[99],"properties":[100],"their":[102],"matrices.":[105]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
