{"id":"https://openalex.org/W2290373954","doi":"https://doi.org/10.37236/5631","title":"Web Matrices: Structural Properties and Generating Combinatorial Identities","display_name":"Web Matrices: Structural Properties and Generating Combinatorial Identities","publication_year":2016,"publication_date":"2016-03-04","ids":{"openalex":"https://openalex.org/W2290373954","doi":"https://doi.org/10.37236/5631","mag":"2290373954"},"language":"en","primary_location":{"id":"doi:10.37236/5631","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5631","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p45/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/v23i1p45/pdf","any_repository_has_fulltext":true},"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"]},{"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"]}],"countries":["CL","GB"],"is_corresponding":true,"raw_author_name":"Mark Dukes","raw_affiliation_strings":["University of Strathclyde","Computer And Information Sciences"],"affiliations":[{"raw_affiliation_string":"University of Strathclyde","institution_ids":["https://openalex.org/I181647926"]},{"raw_affiliation_string":"Computer And Information Sciences","institution_ids":["https://openalex.org/I3130035786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048139332","display_name":"Chris D. White","orcid":"https://orcid.org/0000-0002-6752-2394"},"institutions":[{"id":"https://openalex.org/I7882870","display_name":"University of Glasgow","ror":"https://ror.org/00vtgdb53","country_code":"GB","type":"education","lineage":["https://openalex.org/I7882870"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Chris D White","raw_affiliation_strings":["University of Glasgow","*University of Glasgow"],"affiliations":[{"raw_affiliation_string":"University of Glasgow","institution_ids":["https://openalex.org/I7882870"]},{"raw_affiliation_string":"*University of Glasgow","institution_ids":["https://openalex.org/I7882870"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5054414618"],"corresponding_institution_ids":["https://openalex.org/I181647926","https://openalex.org/I3130035786"],"apc_list":null,"apc_paid":null,"fwci":0.6865,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.67515617,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"23","issue":"1","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":0.9969000220298767,"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":0.9969000220298767,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10025","display_name":"Black Holes and Theoretical Physics","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4651772677898407},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.45544174313545227},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43255746364593506},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.41611015796661377},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3701589107513428}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4651772677898407},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.45544174313545227},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43255746364593506},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.41611015796661377},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3701589107513428},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/5631","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5631","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p45/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:strathprints.strath.ac.uk:55768","is_oa":false,"landing_page_url":"https://strathprints.strath.ac.uk/view/author/792674.html>","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":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:arXiv.org:1603.01589","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1603.01589","pdf_url":"https://arxiv.org/pdf/1603.01589","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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.1603.01589","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1603.01589","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-journal"},{"id":"mag:2290373954","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"doi:10.37236/5631","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5631","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p45/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/G7130012615","display_name":null,"funder_award_id":"ST/L000466/1","funder_id":"https://openalex.org/F4320334632","funder_display_name":"Science and Technology Facilities Council"}],"funders":[{"id":"https://openalex.org/F4320334632","display_name":"Science and Technology Facilities Council","ror":"https://ror.org/057g20z61"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2290373954.pdf","grobid_xml":"https://content.openalex.org/works/W2290373954.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1556399213","https://openalex.org/W1863709358","https://openalex.org/W1959774252","https://openalex.org/W1977531989","https://openalex.org/W1979423085","https://openalex.org/W2009309337","https://openalex.org/W2016756317","https://openalex.org/W2026055387","https://openalex.org/W2028466525","https://openalex.org/W2029948740","https://openalex.org/W2046954180","https://openalex.org/W2048548096","https://openalex.org/W2072587729","https://openalex.org/W2124621104","https://openalex.org/W2133338173","https://openalex.org/W2150218434","https://openalex.org/W2914994214","https://openalex.org/W3098087372","https://openalex.org/W3103297238","https://openalex.org/W3106259061","https://openalex.org/W6652840411","https://openalex.org/W6662240018","https://openalex.org/W6682152674","https://openalex.org/W6759523886","https://openalex.org/W6785404918","https://openalex.org/W6785940558"],"related_works":["https://openalex.org/W2964307238","https://openalex.org/W3194352924","https://openalex.org/W2463887868","https://openalex.org/W2763556869","https://openalex.org/W2889634852","https://openalex.org/W2949520616","https://openalex.org/W3140307183","https://openalex.org/W2047815507","https://openalex.org/W2887061492","https://openalex.org/W2306587635","https://openalex.org/W3124125214","https://openalex.org/W16939786","https://openalex.org/W2106050097","https://openalex.org/W2950395448","https://openalex.org/W2072338702","https://openalex.org/W40978292","https://openalex.org/W203890669","https://openalex.org/W1838030851","https://openalex.org/W3007353884","https://openalex.org/W3099190048"],"abstract_inverted_index":{"In":[0],"this":[1,256],"paper":[2],"we":[3,89],"present":[4,126,181],"new":[5,103],"results":[6,95,128],"for":[7,105,222],"the":[8,23,53,58,65,69,81,97,111,115,120,136,151,154,163,188,201,204,207,219,251],"combinatorics":[9,262],"of":[10,25,47,55,57,84,114,141,157,185,187,203,206,232],"web":[11,14,40,60,86,137,146,179,239],"diagrams":[12],"and":[13,34,49,76,247],"worlds.":[15,87],"These":[16],"are":[17,42,162],"discrete":[18],"objects":[19],"that":[20,62,91,133,217,241],"arise":[21],"in":[22,29,135,172,226,255],"physics":[24],"calculating":[26],"scattering":[27],"amplitudes":[28],"non-abelian":[30],"gauge":[31],"theories.":[32],"Web-colouring":[33],"web-mixing":[35,189],"matrices":[36],"(collectively":[37],"known":[38,93],"as":[39],"matrices)":[41],"indexed":[43],"by":[44,213],"ordered":[45],"pairs":[46],"web-diagrams":[48],"contain":[50],"information":[51],"relating":[52],"number":[54],"colourings":[56],"first":[59,140],"diagram":[61],"will":[63,149],"produce":[64],"second":[66,166],"diagram.We":[67],"introduce":[68],"black":[70,98],"diamond":[71,99],"product":[72,100,116],"on":[73,117,178],"power":[74,118,224],"series":[75,225],"show":[77,90,199,248],"how":[78,144,200,249],"it":[79],"determines":[80],"web-colouring":[82,208,252],"matrix":[83,147,209,253],"disjoint":[85],"Furthermore,":[88],"combining":[92],"physical":[94,194],"with":[96,174],"gives":[101],"a":[102,175,182,214,230,261],"technique":[104],"generating":[106],"combinatorial":[107,183],"identities.":[108],"Due":[109],"to":[110,129,229,244,260],"complicated":[112],"action":[113],"series,":[119],"resulting":[121],"identities":[122],"appear":[123,134],"highly":[124],"non-trivial.We":[125],"two":[127],"explain":[130],"repeated":[131,170],"entries":[132,148,171,202,254],"matrices.":[138],"The":[139,165],"these":[142],"shows":[143],"diagonal":[145],"be":[150,211],"same":[152],"if":[153],"comparability":[155],"graphs":[156],"their":[158],"associated":[159],"decomposition":[160],"posets":[161],"same.":[164],"result":[167],"concerns":[168],"general":[169],"conjunction":[173],"flipping":[176],"operation":[177],"diagrams.We":[180],"proof":[184],"idempotency":[186],"matrices,":[190],"previously":[191],"established":[192],"using":[193],"arguments":[195],"only.":[196],"We":[197,234],"also":[198],"square":[205],"can":[210],"achieved":[212],"linear":[215],"transformation":[216],"maps":[218],"standard":[220],"basis":[221],"formal":[223],"one":[227,237],"variable":[228],"sequence":[231],"polynomials.":[233],"look":[235],"at":[236],"parameterized":[238],"world":[240],"is":[242,258],"related":[243],"indecomposable":[245],"permutations":[246],"determining":[250],"case":[257],"equivalent":[259],"onwords":[263],"problem.":[264]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
