{"id":"https://openalex.org/W2169694889","doi":"https://doi.org/10.1017/s0963548311000393","title":"A Graph Integral Formulation of the Circuit Partition Polynomial","display_name":"A Graph Integral Formulation of the Circuit Partition Polynomial","publication_year":2011,"publication_date":"2011-10-11","ids":{"openalex":"https://openalex.org/W2169694889","doi":"https://doi.org/10.1017/s0963548311000393","mag":"2169694889"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548311000393","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548311000393","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008033989","display_name":"Cristopher Moore","orcid":"https://orcid.org/0000-0002-2062-1942"},"institutions":[{"id":"https://openalex.org/I1308548392","display_name":"Santa Fe Institute","ror":"https://ror.org/01arysc35","country_code":"US","type":"funder","lineage":["https://openalex.org/I1308548392"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"CRISTOPHER MOORE","raw_affiliation_strings":["Computer Science Department, University of New Mexico, Albuquerque, NM 87131, USA and The Santa Fe Institute, Santa Fe, NM 87501, USA (e-mail:","Computer science department, university of new mexico, albuquerque, nm 87131, usa and the santa fe institute, santa fe, nm 87501, usa (e-mail: moore@santafe.edu)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Department, University of New Mexico, Albuquerque, NM 87131, USA and The Santa Fe Institute, Santa Fe, NM 87501, USA (e-mail:","institution_ids":["https://openalex.org/I1308548392"]},{"raw_affiliation_string":"Computer science department, university of new mexico, albuquerque, nm 87131, usa and the santa fe institute, santa fe, nm 87501, usa (e-mail: moore@santafe.edu)#TAB#","institution_ids":["https://openalex.org/I1308548392"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088846595","display_name":"Alexander Russell","orcid":"https://orcid.org/0000-0002-8228-6238"},"institutions":[{"id":"https://openalex.org/I140172145","display_name":"University of Connecticut","ror":"https://ror.org/02der9h97","country_code":"US","type":"education","lineage":["https://openalex.org/I140172145"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"ALEXANDER RUSSELL","raw_affiliation_strings":["Department of Computer Science & Engineering, University of Connecticut, Storrs, CT 06269, USA (e-mail:","Department of computer science & engineering, university of connecticut, storrs, ct 06269, usa (e-mail: acr@cse.uconn.edu)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science & Engineering, University of Connecticut, Storrs, CT 06269, USA (e-mail:","institution_ids":["https://openalex.org/I140172145"]},{"raw_affiliation_string":"Department of computer science & engineering, university of connecticut, storrs, ct 06269, usa (e-mail: acr@cse.uconn.edu)#TAB#","institution_ids":["https://openalex.org/I140172145"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.19468444,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"20","issue":"6","first_page":"911","last_page":"920"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":1.0,"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/T11476","display_name":"Graph theory and applications","score":1.0,"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":0.9998000264167786,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9994999766349792,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.743518590927124},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6780178546905518},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.6540115475654602},{"id":"https://openalex.org/keywords/integral-graph","display_name":"Integral graph","score":0.6020389795303345},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5657818913459778},{"id":"https://openalex.org/keywords/frequency-partition-of-a-graph","display_name":"Frequency partition of a graph","score":0.5311607122421265},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.515235960483551},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4672142565250397},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4613404870033264},{"id":"https://openalex.org/keywords/simple-graph","display_name":"Simple graph","score":0.45248040556907654},{"id":"https://openalex.org/keywords/graph-partition","display_name":"Graph partition","score":0.43878331780433655},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.24232783913612366},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14429020881652832},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.127358078956604}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.743518590927124},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6780178546905518},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6540115475654602},{"id":"https://openalex.org/C204710682","wikidata":"https://www.wikidata.org/wiki/Q3036983","display_name":"Integral graph","level":5,"score":0.6020389795303345},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5657818913459778},{"id":"https://openalex.org/C178744013","wikidata":"https://www.wikidata.org/wiki/Q5502876","display_name":"Frequency partition of a graph","level":5,"score":0.5311607122421265},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.515235960483551},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4672142565250397},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4613404870033264},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.45248040556907654},{"id":"https://openalex.org/C48903430","wikidata":"https://www.wikidata.org/wiki/Q491370","display_name":"Graph partition","level":3,"score":0.43878331780433655},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.24232783913612366},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14429020881652832},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.127358078956604}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0963548311000393","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548311000393","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1590902061","https://openalex.org/W1968273868","https://openalex.org/W1987955590","https://openalex.org/W2011473996","https://openalex.org/W2015927509","https://openalex.org/W2016645081","https://openalex.org/W2028239976","https://openalex.org/W2074878962","https://openalex.org/W2086681482","https://openalex.org/W2086735515","https://openalex.org/W2110055721","https://openalex.org/W2110841914","https://openalex.org/W2247216366","https://openalex.org/W2896866551","https://openalex.org/W2992527946","https://openalex.org/W4234397156","https://openalex.org/W6771075664"],"related_works":["https://openalex.org/W3139829055","https://openalex.org/W1982865350","https://openalex.org/W3183075326","https://openalex.org/W4300494273","https://openalex.org/W2615015219","https://openalex.org/W2753620285","https://openalex.org/W2168495785","https://openalex.org/W3012931947","https://openalex.org/W2583811263","https://openalex.org/W2035944803"],"abstract_inverted_index":{"We":[0,48,80,112],"present":[1],"a":[2,8,18,25],"simple":[3],"graph":[4],"integral":[5],"equivalent":[6],"to":[7,54,89],"multiple":[9],"of":[10,33,45,59,69],"the":[11,56,60,70,115,121,129],"circuit":[12],"partition":[13,93],"polynomial.":[14],"Let":[15],"G":[16,34,90],"be":[17,24,55],"directed":[19],"graph,":[20],"and":[21,95],"let":[22],"k":[23,39,109],"positive":[26],"integer.":[27],"Associate":[28],"with":[29],"each":[30],"vertex":[31],"v":[32,44,67,78,123],"an":[35],"independent,":[36],"uniformly":[37],"random":[38],"-dimensional":[40],"complex":[41],"vector":[42],"x":[43,74,77,122],"unit":[46],"length.":[47],"define":[49],"q":[50,83,99],"(":[51,65,84,100],"G;k":[52,85,101],")":[53,86,102],"expected":[57],"value":[58],"product,":[61],"over":[62],"all":[63],"edges":[64],"u,":[66],"),":[68],"inner":[71],"product":[72],"\u3008":[73],"u":[75],",":[76],"\u3009.":[79],"show":[81],"that":[82,97,118],"is":[87,103],"proportional":[88],"'s":[91],"cycle":[92],"polynomial,":[94],"therefore":[96],"computing":[98],"#":[104],"P":[105],"-complete":[106],"for":[107],"any":[108],"&gt;":[110],"1.":[111],"also":[113],"study":[114],"natural":[116],"variants":[117],"arise":[119],"when":[120],"are":[124],"real":[125],"or":[126],"drawn":[127],"from":[128],"Gaussian":[130],"distribution.":[131]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
