{"id":"https://openalex.org/W2016930771","doi":"https://doi.org/10.1155/2013/743734","title":"A Framework for Coxeter Spectral Classification of Finite Posets and Their Mesh Geometries of Roots","display_name":"A Framework for Coxeter Spectral Classification of Finite Posets and Their Mesh Geometries of Roots","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2016930771","doi":"https://doi.org/10.1155/2013/743734","mag":"2016930771"},"language":"en","primary_location":{"id":"doi:10.1155/2013/743734","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/743734","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2013/743734.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2013/743734.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008584401","display_name":"Daniel Simson","orcid":"https://orcid.org/0000-0002-9610-1476"},"institutions":[{"id":"https://openalex.org/I3019271933","display_name":"Nicolaus Copernicus University","ror":"https://ror.org/0102mm775","country_code":"PL","type":"education","lineage":["https://openalex.org/I3019271933"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Daniel Simson","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Ulica Chopina 12/18, 87-100 Toru\u0144, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Ulica Chopina 12/18, 87-100 Toru\u0144, Poland","institution_ids":["https://openalex.org/I3019271933"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020524796","display_name":"Katarzyna Zaj\u0105c","orcid":"https://orcid.org/0000-0003-4139-9276"},"institutions":[{"id":"https://openalex.org/I3019271933","display_name":"Nicolaus Copernicus University","ror":"https://ror.org/0102mm775","country_code":"PL","type":"education","lineage":["https://openalex.org/I3019271933"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Katarzyna Zaj\u0105c","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Ulica Chopina 12/18, 87-100 Toru\u0144, Poland"],"raw_orcid":"https://orcid.org/0000-0003-4139-9276","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Ulica Chopina 12/18, 87-100 Toru\u0144, Poland","institution_ids":["https://openalex.org/I3019271933"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I3019271933"],"apc_list":{"value":1240,"currency":"USD","value_usd":1240},"apc_paid":{"value":1240,"currency":"USD","value_usd":1240},"fwci":7.1151,"has_fulltext":true,"cited_by_count":24,"citation_normalized_percentile":{"value":0.97587395,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"22"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9998999834060669,"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/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/T11673","display_name":"Advanced Topics in Algebra","score":0.9976999759674072,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5654894709587097},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.37945136427879333},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32833611965179443}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5654894709587097},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.37945136427879333},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32833611965179443}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2013/743734","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/743734","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2013/743734.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:743734","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2013/743734.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:ff9e68bcaf0f4ccdb15e5f233086e211","is_oa":false,"landing_page_url":"https://doaj.org/article/ff9e68bcaf0f4ccdb15e5f233086e211","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/743734","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/743734","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2013/743734.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2016930771.pdf","grobid_xml":"https://content.openalex.org/works/W2016930771.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W1480516528","https://openalex.org/W1493438896","https://openalex.org/W1511069853","https://openalex.org/W1553753142","https://openalex.org/W1557075399","https://openalex.org/W1867752094","https://openalex.org/W1880646138","https://openalex.org/W1933165643","https://openalex.org/W1974385789","https://openalex.org/W1985717197","https://openalex.org/W1987885619","https://openalex.org/W1989125084","https://openalex.org/W1993769788","https://openalex.org/W1999102455","https://openalex.org/W2001484083","https://openalex.org/W2010828954","https://openalex.org/W2014015117","https://openalex.org/W2021515518","https://openalex.org/W2025140234","https://openalex.org/W2028449252","https://openalex.org/W2046345195","https://openalex.org/W2051738830","https://openalex.org/W2053947494","https://openalex.org/W2061472895","https://openalex.org/W2066818605","https://openalex.org/W2077287033","https://openalex.org/W2079333407","https://openalex.org/W2080860082","https://openalex.org/W2092619942","https://openalex.org/W2093738880","https://openalex.org/W2167157837","https://openalex.org/W2313352869","https://openalex.org/W2503589681","https://openalex.org/W3102938051","https://openalex.org/W3103951057","https://openalex.org/W4210751359","https://openalex.org/W4300824122"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2317200988","https://openalex.org/W2376932109","https://openalex.org/W2382290278","https://openalex.org/W2350741829"],"abstract_inverted_index":{"Following":[0,83],"our":[1],"paper":[2],"[Linear":[3,249],"Algebra":[4,250],"Appl.":[5,49,251],"433(2010),":[6],"699\u2013717],":[7],"we":[8,90,121,167,239],"present":[9],"a":[10,57,104,110,126,146,183,231],"framework":[11],"and":[12,109,132,152,247],"computational":[13],"tools":[14],"for":[15,30,255],"the":[16,27,31,66,77,84,133,141,149,169,174,178,196,207,210,224,242],"Coxeter":[17,58,95,100,105,111,128,142,170,179,197,211],"spectral":[18,59,171,180,198],"classification":[19,60],"of":[20,26,36,39,61,80,86,148,154,156,164,173,182,195,200,215],"finite":[21],"posets":[22,40,62,175,202],"J\u2261(J,\u2aaf)":[23],".":[24,82,114,137,192],"One":[25],"main":[28],"motivations":[29],"study":[32],"is":[33,71,76,118,145,161,204,263],"an":[34],"application":[35],"matrix":[37,69,79,96,220,259],"representations":[38],"in":[41,56],"representation":[42],"theory":[43],"explained":[44],"by":[45,245],"Drozd":[46,87],"[Funct.":[47],"Anal.":[48],"8(1974),":[50],"219\u2013225].":[51],"We":[52],"are":[53],"mainly":[54],"interested":[55],"J":[63,81,93,125,176,191,203,216,226],"such":[64,201],"that":[65],"symmetric":[67],"Gram":[68],"GJ:=(1/2)[CJ+CJtr]\u2208\ud835\udd44J(\u211a)":[70],"positive":[72,119,162],"semidefinite,":[73],"where":[74],"CJ\u2208\ud835\udd44J(\u2124)":[75],"incidence":[78,219],"idea":[85],"mentioned":[88],"earlier,":[89],"associate":[91,123],"to":[92,124,205,230],"its":[94,99,218],"CoxJ:=-CJ\u00b7CJ-tr":[97],",":[98,103,108,131,261],"spectrum":[101,143],"speccJ":[102,144],"polynomial":[106],"coxJ(t)\u2208\u2124[t]":[107],"number":[112,129],"cJ":[113],"In":[115,138,158,234],"case":[116,159],"GJ":[117,160],"semi-definite,":[120],"also":[122,240],"reduced":[127],"c\u030cJ":[130],"defect":[134],"homomorphism":[135],"\u2202J:\u2124J\u2192\u2124":[136],"this":[139,237],"case,":[140],"subset":[147],"unit":[150],"circle":[151],"consists":[153],"roots":[155],"unity.":[157],"semi-definite":[163],"corank":[165],"one,":[166],"relate":[168],"properties":[172,181],"with":[177,190,236],"simply":[184],"laced":[185],"Euclidean":[186],"diagram":[187],"DJ\u2208{\ud835\udd3b\u0303n,\ud835\udd3c\u03036,\ud835\udd3c\u03037,\ud835\udd3c\u03038}":[188],"associated":[189],"Our":[193],"aim":[194],"analysis":[199],"answer":[206],"question":[208],"when":[209],"type":[212],"CtypeJ:=(speccJ,cJ,":[213],"c\u030cJ)":[214],"determines":[217],"CJ":[221],"(and,":[222],"hence,":[223],"poset":[225],")":[227],"uniquely,":[228],"up":[229],"\u2124":[232,257],"-congruency.":[233],"connection":[235],"question,":[238],"discuss":[241],"problem":[243],"studied":[244],"Horn":[246],"Sergeichuk":[248],"389(2004),":[252],"347\u2013353],":[253],"if":[254],"any":[256],"-invertible":[258],"A\u2208\ud835\udd44n(\u2124)":[260],"there":[262],"B\u2208\ud835\udd44n<":[264]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}