{"id":"https://openalex.org/W1513678316","doi":"https://doi.org/10.37236/647","title":"On Multivariate Chromatic Polynomials of Hypergraphs and Hyperedge Elimination","display_name":"On Multivariate Chromatic Polynomials of Hypergraphs and Hyperedge Elimination","publication_year":2011,"publication_date":"2011-08-05","ids":{"openalex":"https://openalex.org/W1513678316","doi":"https://doi.org/10.37236/647","mag":"1513678316"},"language":"en","primary_location":{"id":"doi:10.37236/647","is_oa":true,"landing_page_url":"https://doi.org/10.37236/647","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p160/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/v18i1p160/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101908898","display_name":"Jacob A. White","orcid":"https://orcid.org/0000-0002-2589-1087"},"institutions":[{"id":"https://openalex.org/I73544541","display_name":"Mathematical Sciences Research Institute","ror":"https://ror.org/05hs5r386","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I73544541"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jacob A. White","raw_affiliation_strings":["Mathematical Sciences Research Institute Berkeley, California, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Sciences Research Institute Berkeley, California, USA","institution_ids":["https://openalex.org/I73544541"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101908898"],"corresponding_institution_ids":["https://openalex.org/I73544541"],"apc_list":null,"apc_paid":null,"fwci":3.1331,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.89675608,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998000264167786,"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":0.9998000264167786,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9790999889373779,"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/T11106","display_name":"Data Management and Algorithms","score":0.9678000211715698,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/mathematics","display_name":"Mathematics","score":0.8310725092887878},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6688857078552246},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.640586256980896},{"id":"https://openalex.org/keywords/chromatic-polynomial","display_name":"Chromatic polynomial","score":0.5940585136413574},{"id":"https://openalex.org/keywords/polynomial-matrix","display_name":"Polynomial matrix","score":0.5162708759307861},{"id":"https://openalex.org/keywords/difference-polynomials","display_name":"Difference polynomials","score":0.47674310207366943},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4735026955604553},{"id":"https://openalex.org/keywords/tutte-polynomial","display_name":"Tutte polynomial","score":0.4734846353530884},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.462190717458725},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.4539903402328491},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.2647898197174072},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.24505627155303955},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.19475415349006653},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.05994606018066406}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8310725092887878},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6688857078552246},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.640586256980896},{"id":"https://openalex.org/C126385604","wikidata":"https://www.wikidata.org/wiki/Q1087609","display_name":"Chromatic polynomial","level":3,"score":0.5940585136413574},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.5162708759307861},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.47674310207366943},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4735026955604553},{"id":"https://openalex.org/C14447369","wikidata":"https://www.wikidata.org/wiki/Q7857002","display_name":"Tutte polynomial","level":5,"score":0.4734846353530884},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.462190717458725},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.4539903402328491},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.2647898197174072},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.24505627155303955},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.19475415349006653},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.05994606018066406},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/647","is_oa":true,"landing_page_url":"https://doi.org/10.37236/647","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p160/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:10.37236/647","is_oa":true,"landing_page_url":"https://doi.org/10.37236/647","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p160/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/G4691065209","display_name":null,"funder_award_id":"0932078","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6128562221","display_name":null,"funder_award_id":"DMS-0932078","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"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1513678316.pdf","grobid_xml":"https://content.openalex.org/works/W1513678316.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1530753374","https://openalex.org/W1531965102","https://openalex.org/W1968703234","https://openalex.org/W2033325972","https://openalex.org/W2050882124","https://openalex.org/W2090732476","https://openalex.org/W2092277386","https://openalex.org/W2152710849","https://openalex.org/W2159018842","https://openalex.org/W2570395877","https://openalex.org/W2962809359","https://openalex.org/W4232224617","https://openalex.org/W4232649250"],"related_works":["https://openalex.org/W4211170257","https://openalex.org/W2527934888","https://openalex.org/W4302506957","https://openalex.org/W2953032778","https://openalex.org/W2026073766","https://openalex.org/W2073184325","https://openalex.org/W593587541","https://openalex.org/W1531965102","https://openalex.org/W2964638337","https://openalex.org/W2017373798"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,114,129],"introduce":[4],"multivariate":[5,10,38],"hyperedge":[6,79,132],"elimination":[7,133],"polynomials":[8,12,19,74,76,97,117],"and":[9,35,50,57,65,83,113,135],"chromatic":[11,39,60,138],"for":[13,30,118],"hypergraphs.":[14,122],"The":[15,37],"first":[16],"set":[17],"of":[18,24,48,55,62,71,103,110,121],"is":[20,41],"defined":[21,45,100],"in":[22,46,101],"terms":[23,47,102],"a":[25,111],"deletion-contraction-extraction":[26],"recurrence,":[27],"previously":[28],"investigated":[29],"graphs":[31],"by":[32],"Averbouch,":[33],"Godlin,":[34],"Makowsky.":[36],"polynomial":[40,44,54,61,134],"an":[42],"equivalent":[43],"colorings,":[49],"generalizes":[51],"the":[52,58,96,107,131,136],"coboundary":[53],"Crapo,":[56],"bivariate":[59],"Dohmen,":[63],"P\u00f6nitz":[64],"Tittman.":[66],"We":[67,92,123],"prove":[68,94],"that":[69,95],"specializations":[70],"these":[72,116],"new":[73],"recover":[75],"which":[77,128],"enumerate":[78],"coverings,":[80],"matchings,":[81],"transversals,":[82],"section":[84],"hypergraphs,":[85],"all":[86],"weighted":[87],"according":[88],"to":[89],"certain":[90],"statistics.":[91],"also":[93,124],"can":[98],"be":[99],"M\u00f6bius":[104],"inversion":[105],"on":[106],"partition":[108],"lattice":[109],"hypergraph,":[112],"compute":[115],"various":[119],"classes":[120],"consider":[125],"trivariate":[126,137],"polynomials,":[127],"call":[130],"polynomial.":[139]},"counts_by_year":[{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":4}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
