{"id":"https://openalex.org/W2921149331","doi":"https://doi.org/10.37236/8759","title":"Root Cones and the Resonance Arrangement","display_name":"Root Cones and the Resonance Arrangement","publication_year":2021,"publication_date":"2021-01-14","ids":{"openalex":"https://openalex.org/W2921149331","doi":"https://doi.org/10.37236/8759","mag":"2921149331"},"language":"en","primary_location":{"id":"doi:10.37236/8759","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8759","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p12/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/v28i1p12/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044065045","display_name":"Samuel C. Gutekunst","orcid":"https://orcid.org/0000-0002-3516-2996"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Samuel C. Gutekunst","raw_affiliation_strings":["Operations Research and Information Engineering, Cornell University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Operations Research and Information Engineering, Cornell University","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037990830","display_name":"Karola M\u00e9sz\u00e1ros","orcid":null},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Karola M\u00e9sz\u00e1ros","raw_affiliation_strings":["Department of Mathematics, Cornell University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Cornell University","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015920373","display_name":"T. Kyle Petersen","orcid":"https://orcid.org/0000-0001-5188-6049"},"institutions":[{"id":"https://openalex.org/I118353179","display_name":"DePaul University","ror":"https://ror.org/04xtx5t16","country_code":"US","type":"education","lineage":["https://openalex.org/I118353179"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"T. Kyle Petersen","raw_affiliation_strings":["Department of Mathematical Sciences, DePaul University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, DePaul University","institution_ids":["https://openalex.org/I118353179"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5044065045"],"corresponding_institution_ids":["https://openalex.org/I205783295"],"apc_list":null,"apc_paid":null,"fwci":1.2924,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.7089372,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"28","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":1.0,"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":1.0,"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":0.9921000003814697,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9891999959945679,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/hyperplane","display_name":"Hyperplane","score":0.8766114115715027},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.7078894376754761},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.7029890418052673},{"id":"https://openalex.org/keywords/resonance","display_name":"Resonance (particle physics)","score":0.6700164675712585},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5821621417999268},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.5399181842803955},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5392137765884399},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.47982144355773926},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.44368305802345276},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.27716583013534546},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2165473997592926}],"concepts":[{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.8766114115715027},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.7078894376754761},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.7029890418052673},{"id":"https://openalex.org/C139210041","wikidata":"https://www.wikidata.org/wiki/Q2145840","display_name":"Resonance (particle physics)","level":2,"score":0.6700164675712585},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5821621417999268},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.5399181842803955},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5392137765884399},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.47982144355773926},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.44368305802345276},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.27716583013534546},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2165473997592926},{"id":"https://openalex.org/C109214941","wikidata":"https://www.wikidata.org/wiki/Q18334","display_name":"Particle physics","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/8759","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8759","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p12/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:arXiv.org:1903.06595","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1903.06595","pdf_url":"https://arxiv.org/pdf/1903.06595","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":"","raw_type":"text"},{"id":"mag:2921149331","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1903.06595.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1903.06595","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1903.06595","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"}],"best_oa_location":{"id":"doi:10.37236/8759","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8759","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p12/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/G105238394","display_name":null,"funder_award_id":"DGE-1650441","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3447873124","display_name":null,"funder_award_id":"-1650441","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7031722743","display_name":null,"funder_award_id":"1650441","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G762668318","display_name":null,"funder_award_id":"DMS 1847284","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8363043069","display_name":null,"funder_award_id":"DMS 1501059","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8737478189","display_name":"Polytopes in Combinatorics and Algebra","funder_award_id":"1501059","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/F4320307521","display_name":"American Institute of Mathematics","ror":"https://ror.org/02a0fwv66"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2921149331.pdf","grobid_xml":"https://content.openalex.org/works/W2921149331.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W19601023","https://openalex.org/W1556866066","https://openalex.org/W1609370892","https://openalex.org/W1654330493","https://openalex.org/W1670162102","https://openalex.org/W1991964142","https://openalex.org/W1998788558","https://openalex.org/W2008119321","https://openalex.org/W2015190299","https://openalex.org/W2016078847","https://openalex.org/W2056585184","https://openalex.org/W2082196278","https://openalex.org/W2092636674","https://openalex.org/W2109513701","https://openalex.org/W2130025413","https://openalex.org/W2130848020","https://openalex.org/W2147658430","https://openalex.org/W2148613317","https://openalex.org/W2154525883","https://openalex.org/W2466462182","https://openalex.org/W2612230526","https://openalex.org/W2780310943","https://openalex.org/W2807218142","https://openalex.org/W2895314891","https://openalex.org/W2910042527","https://openalex.org/W2963038754","https://openalex.org/W3020877381","https://openalex.org/W3097613963","https://openalex.org/W3104949781","https://openalex.org/W4248545690","https://openalex.org/W6637020025","https://openalex.org/W6637167610","https://openalex.org/W6664578703","https://openalex.org/W6671129580","https://openalex.org/W6682158213","https://openalex.org/W6793567120"],"related_works":["https://openalex.org/W3118319930","https://openalex.org/W3081346619","https://openalex.org/W1629162631","https://openalex.org/W2132344168","https://openalex.org/W87871152","https://openalex.org/W2040891755","https://openalex.org/W2067004904","https://openalex.org/W2775228770","https://openalex.org/W1997625405","https://openalex.org/W1981436438","https://openalex.org/W2954630797","https://openalex.org/W2931792776","https://openalex.org/W2062291935","https://openalex.org/W3104455254","https://openalex.org/W2002300566","https://openalex.org/W1575239777","https://openalex.org/W37461142","https://openalex.org/W2787011530","https://openalex.org/W2755845273","https://openalex.org/W2738991358"],"abstract_inverted_index":{"We":[0,51],"study":[1],"the":[2,13,33,36,47,74,77,87,100,109,114,119,124,137,141],"connection":[3],"between":[4,126],"triangulations":[5],"of":[6,26,38,65,76,111,113,140,143],"a":[7,16,23],"type":[8],"$A$":[9],"root":[10,101],"polytope":[11,102],"and":[12,63,129],"resonance":[14,34,39,78,106,127,144],"arrangement,":[15,35,79],"hyperplane":[17,120],"arrangement":[18],"that":[19,136],"shows":[20],"up":[21,45],"in":[22,81],"surprising":[24],"number":[25,37,142],"contexts.":[27],"Despite":[28],"an":[29,69],"elementary":[30],"definition":[31],"for":[32,56],"chambers":[40,107,110,128,145],"has":[41],"only":[42],"been":[43],"computed":[44],"to":[46,108],"$n=8$":[48],"dimensional":[49],"case.":[50],"focus":[52],"on":[53],"data":[54],"structures":[55],"labeling":[57],"chambers,":[58],"such":[59],"as":[60],"sign":[61],"vectors":[62],"sets":[64],"alternating":[66],"trees,":[67],"with":[68,92],"aim":[70],"at":[71],"better":[72],"understanding":[73],"structure":[75],"and,":[80],"particular,":[82,133],"enumerating":[83],"its":[84],"chambers.":[85],"Along":[86],"way,":[88],"we":[89,104,122,134],"make":[90],"connections":[91,125],"similar":[93],"(and":[94],"similarly":[95],"difficult)":[96],"enumeration":[97],"questions.":[98],"With":[99,118],"viewpoint,":[103,121],"relate":[105],"polynomiality":[112],"Kostant":[115],"partition":[116],"function.":[117],"clarify":[123],"threshold":[130],"functions.":[131],"In":[132],"show":[135],"base-2":[138],"logarithm":[139],"is":[146],"asymptotically":[147],"$n^2$.":[148]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
