{"id":"https://openalex.org/W3045121045","doi":"https://doi.org/10.37236/9768","title":"Computing Volumes of Adjacency Polytopes via Draconian Sequences","display_name":"Computing Volumes of Adjacency Polytopes via Draconian Sequences","publication_year":2022,"publication_date":"2022-03-25","ids":{"openalex":"https://openalex.org/W3045121045","doi":"https://doi.org/10.37236/9768","mag":"3045121045"},"language":"en","primary_location":{"id":"doi:10.37236/9768","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9768","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i1p61/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":"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/v29i1p61/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023245544","display_name":"Robert Davis","orcid":"https://orcid.org/0000-0002-4015-1773"},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Robert Davis","raw_affiliation_strings":["Michigan State University"],"affiliations":[{"raw_affiliation_string":"Michigan State University","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101634382","display_name":"Tianran Chen","orcid":"https://orcid.org/0000-0002-3890-617X"},"institutions":[{"id":"https://openalex.org/I902671590","display_name":"Auburn University at Montgomery","ror":"https://ror.org/05eynd241","country_code":"US","type":"education","lineage":["https://openalex.org/I902671590"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tianran Chen","raw_affiliation_strings":["Auburn University at Montgomery"],"affiliations":[{"raw_affiliation_string":"Auburn University at Montgomery","institution_ids":["https://openalex.org/I902671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023245544"],"corresponding_institution_ids":["https://openalex.org/I87216513"],"apc_list":null,"apc_paid":null,"fwci":1.7056,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.77690468,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"29","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":0.9968000054359436,"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":0.9968000054359436,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.988099992275238,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9843999743461609,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/polytope","display_name":"Polytope","score":0.8447939157485962},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7906914949417114},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.738427460193634},{"id":"https://openalex.org/keywords/adjacency-list","display_name":"Adjacency list","score":0.7104535102844238},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.658475399017334},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6260460019111633},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.5470590591430664},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4207271933555603},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4131707549095154}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.8447939157485962},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7906914949417114},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.738427460193634},{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.7104535102844238},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.658475399017334},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6260460019111633},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.5470590591430664},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4207271933555603},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4131707549095154}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/9768","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9768","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i1p61/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"}],"best_oa_location":{"id":"doi:10.37236/9768","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9768","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i1p61/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/G1225171536","display_name":null,"funder_award_id":"1923099","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4381486931","display_name":null,"funder_award_id":"1922998","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7277629090","display_name":null,"funder_award_id":"DMS-1922998","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8301408911","display_name":null,"funder_award_id":"DMS-1923099","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"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3045121045.pdf","grobid_xml":"https://content.openalex.org/works/W3045121045.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W39921581","https://openalex.org/W2054260295","https://openalex.org/W2110754991","https://openalex.org/W2130848020","https://openalex.org/W2201597088","https://openalex.org/W2482024337","https://openalex.org/W2752985590","https://openalex.org/W2771128703","https://openalex.org/W2963422512","https://openalex.org/W2963442161","https://openalex.org/W2979958158","https://openalex.org/W3144402195","https://openalex.org/W4221148651","https://openalex.org/W4288797800","https://openalex.org/W4302081240","https://openalex.org/W4307404224"],"related_works":["https://openalex.org/W4280529077","https://openalex.org/W2371352078","https://openalex.org/W2507185596","https://openalex.org/W1493684871","https://openalex.org/W4286224459","https://openalex.org/W2886567582","https://openalex.org/W4289703404","https://openalex.org/W34983847","https://openalex.org/W4285598206","https://openalex.org/W3186549454"],"abstract_inverted_index":{"Adjacency":[0],"polytopes":[1],"appear":[2],"naturally":[3],"in":[4,11,35,42],"the":[5,23,49,63,75,99,128,146,165],"study":[6],"of":[7,25,52,65,77,130,149,155,159,187],"nonlinear":[8],"emergent":[9],"phenomena":[10],"complex":[12],"networks.":[13],"The":[14],"``\"PQ-type\"":[15],"adjacency":[16,55],"polytope,":[17,56],"denoted":[18],"$\\nabla^{\\mathrm{PQ}}_G$":[19,82,150],"and":[20,126],"which":[21,57,190],"is":[22,48,92,153],"focus":[24],"this":[26,70],"work,":[27],"encodes":[28],"rich":[29],"combinatorial":[30],"information":[31],"about":[32],"power-flow":[33,67],"solutions":[34],"sparse":[36],"power":[37],"networks":[38,106],"that":[39,74,164,196],"are":[40,179,191,197],"studied":[41],"electric":[43],"engineering.":[44],"Of":[45],"particular":[46],"importance":[47],"normalized":[50,79,147],"volume":[51,148],"such":[53],"an":[54,59,124,131],"provides":[58],"upper":[60],"bound":[61],"on":[62],"number":[64],"distinct":[66],"solutions.":[68],"In":[69],"article":[71],"we":[72,119,162,182],"show":[73],"problem":[76],"computing":[78],"volumes":[80],"for":[81,104,113,122,145,168,174],"can":[83],"be":[84],"rephrased":[85],"as":[86],"counting":[87],"$D(G)$-draconian":[88],"sequences":[89],"where":[90],"$D(G)$":[91],"a":[93,134,141,156],"certain":[94,117],"bipartite":[95],"graph":[96],"associated":[97],"to":[98],"network.":[100],"We":[101],"prove":[102],"recurrences":[103,121,139],"all":[105,169],"with":[107,133],"connectivity":[108],"at":[109],"most":[110],"$1$":[111],"and,":[112],"$2$-connected":[114],"graphs":[115,188],"under":[116],"restrictions,":[118],"give":[120],"subdividing":[123],"edge":[125,132],"taking":[127],"join":[129],"new":[135],"vertex.":[136],"Together,":[137],"these":[138],"imply":[140],"simple,":[142],"non-recursive":[143],"formula":[144,166],"when":[151],"$G$":[152,189],"part":[154],"large":[157],"class":[158],"outerplanar":[160,170,195],"graphs;":[161],"conjecture":[163],"holds":[167],"graphs.":[171],"Explicit":[172],"formulas":[173],"several":[175,184],"other":[176],"(non-outerplanar)":[177],"classes":[178,186],"given.":[180],"Further,":[181],"identify":[183],"important":[185],"planar":[192],"but":[193],"not":[194],"worth":[198],"additional":[199],"study.":[200]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
