{"id":"https://openalex.org/W3037297578","doi":"https://doi.org/10.37236/9696","title":"A Counterexample to a Conjecture on Schur Positivity of Chromatic Symmetric Functions of trees","display_name":"A Counterexample to a Conjecture on Schur Positivity of Chromatic Symmetric Functions of trees","publication_year":2020,"publication_date":"2020-10-16","ids":{"openalex":"https://openalex.org/W3037297578","doi":"https://doi.org/10.37236/9696","mag":"3037297578"},"language":"en","primary_location":{"id":"doi:10.37236/9696","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9696","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p5/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/v27i4p5/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002875478","display_name":"Emmanuella Sandratra Rambeloson","orcid":null},"institutions":[{"id":"https://openalex.org/I4210112293","display_name":"African Institute for Mathematical Sciences Ghana","ror":"https://ror.org/0231kk931","country_code":"GH","type":"nonprofit","lineage":["https://openalex.org/I4210112293"]}],"countries":["GH"],"is_corresponding":true,"raw_author_name":"Emmanuella Sandratra Rambeloson","raw_affiliation_strings":["African Institute of Mathematical Sciences, Accra, Ghana"],"affiliations":[{"raw_affiliation_string":"African Institute of Mathematical Sciences, Accra, Ghana","institution_ids":["https://openalex.org/I4210112293"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083294700","display_name":"John Shareshian","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"John Shareshian","raw_affiliation_strings":["Washington University"],"affiliations":[{"raw_affiliation_string":"Washington University","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5002875478"],"corresponding_institution_ids":["https://openalex.org/I4210112293"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.21366995,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"4","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":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","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"}},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9264000058174133,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9093000292778015,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.942882776260376},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.8006565570831299},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.718885064125061},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7180851697921753},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.6684166789054871},{"id":"https://openalex.org/keywords/symmetric-function","display_name":"Symmetric function","score":0.5670314431190491},{"id":"https://openalex.org/keywords/schur-polynomial","display_name":"Schur polynomial","score":0.5618064999580383},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4818521738052368},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.45483726263046265},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4343012571334839},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.16997811198234558},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07916858792304993},{"id":"https://openalex.org/keywords/macdonald-polynomials","display_name":"Macdonald polynomials","score":0.0652136504650116},{"id":"https://openalex.org/keywords/jacobi-polynomials","display_name":"Jacobi polynomials","score":0.05559012293815613}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.942882776260376},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8006565570831299},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.718885064125061},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7180851697921753},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.6684166789054871},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.5670314431190491},{"id":"https://openalex.org/C146922319","wikidata":"https://www.wikidata.org/wiki/Q4298935","display_name":"Schur polynomial","level":5,"score":0.5618064999580383},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4818521738052368},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45483726263046265},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4343012571334839},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.16997811198234558},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07916858792304993},{"id":"https://openalex.org/C171686973","wikidata":"https://www.wikidata.org/wiki/Q17098676","display_name":"Macdonald polynomials","level":4,"score":0.0652136504650116},{"id":"https://openalex.org/C48490523","wikidata":"https://www.wikidata.org/wiki/Q371631","display_name":"Jacobi polynomials","level":3,"score":0.05559012293815613},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/9696","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9696","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p5/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:2006.14415","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.14415","pdf_url":"https://arxiv.org/pdf/2006.14415","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":null,"raw_type":"text"},{"id":"mag:3037297578","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/2006.14415.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.2006.14415","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2006.14415","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:10.37236/9696","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9696","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p5/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/G480052443","display_name":null,"funder_award_id":"DMS-1518389","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7473317676","display_name":null,"funder_award_id":"1518389","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3037297578.pdf","grobid_xml":"https://content.openalex.org/works/W3037297578.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W2001124661","https://openalex.org/W2578021995"],"related_works":["https://openalex.org/W3094345885","https://openalex.org/W1999081586","https://openalex.org/W2770880439","https://openalex.org/W2201143618","https://openalex.org/W2951278237","https://openalex.org/W1579025531","https://openalex.org/W2953354481","https://openalex.org/W2278426376","https://openalex.org/W2972027504","https://openalex.org/W2950483934","https://openalex.org/W3214499120","https://openalex.org/W3017712324","https://openalex.org/W2593169963","https://openalex.org/W2031171110","https://openalex.org/W2767880902","https://openalex.org/W2951243968","https://openalex.org/W2554553619","https://openalex.org/W3103872552","https://openalex.org/W2047219167","https://openalex.org/W2513890249"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2],"no":[3],"tree":[4],"on":[5],"twenty":[6],"vertices":[7],"with":[8],"maximum":[9],"degree":[10],"ten":[11],"has":[12],"Schur":[13],"positive":[14],"chromatic":[15],"symmetric":[16],"function,":[17],"thereby":[18],"providing":[19],"a":[20,23],"counterexample":[21],"to":[22],"conjecture":[24],"of":[25],"Dahlberg,":[26],"She":[27],"and":[28],"van":[29],"Willigenburg.":[30]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
