{"id":"https://openalex.org/W4411543102","doi":"https://doi.org/10.1007/s00493-025-00162-2","title":"Local h-polynomials, Uniform Triangulations and Real-rootedness","display_name":"Local h-polynomials, Uniform Triangulations and Real-rootedness","publication_year":2025,"publication_date":"2025-06-23","ids":{"openalex":"https://openalex.org/W4411543102","doi":"https://doi.org/10.1007/s00493-025-00162-2"},"language":"en","primary_location":{"id":"doi:10.1007/s00493-025-00162-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-025-00162-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-025-00162-2.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00493-025-00162-2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009678404","display_name":"Christos A. Athanasiadis","orcid":"https://orcid.org/0000-0001-6860-0748"},"institutions":[{"id":"https://openalex.org/I200777214","display_name":"National and Kapodistrian University of Athens","ror":"https://ror.org/04gnjpq42","country_code":"GR","type":"education","lineage":["https://openalex.org/I200777214"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"Christos A. Athanasiadis","raw_affiliation_strings":["Department of Mathematics, National and Kapodistrian University of Athens, Panepistimioupolis, 15784, Athens, Greece"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National and Kapodistrian University of Athens, Panepistimioupolis, 15784, Athens, Greece","institution_ids":["https://openalex.org/I200777214"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5009678404"],"corresponding_institution_ids":["https://openalex.org/I200777214"],"apc_list":null,"apc_paid":null,"fwci":5.9843,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.94259555,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"45","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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":0.9984999895095825,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9980999827384949,"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/mathematics","display_name":"Mathematics","score":0.8937381505966187},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6840107440948486},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38786354660987854},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3216162621974945}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8937381505966187},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6840107440948486},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38786354660987854},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3216162621974945}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00493-025-00162-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-025-00162-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-025-00162-2.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00493-025-00162-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-025-00162-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-025-00162-2.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320318628","display_name":"Hellenic Academic Libraries Link","ror":null},{"id":"https://openalex.org/F4320323149","display_name":"National and Kapodistrian University of Athens","ror":"https://ror.org/04gnjpq42"},{"id":"https://openalex.org/F4320327859","display_name":"Hellenic Foundation for Research and Innovation","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4411543102.pdf","grobid_xml":"https://content.openalex.org/works/W4411543102.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W652886863","https://openalex.org/W1515761639","https://openalex.org/W1967321127","https://openalex.org/W2024086619","https://openalex.org/W2041179721","https://openalex.org/W2065027287","https://openalex.org/W2069832072","https://openalex.org/W2086949194","https://openalex.org/W2096626276","https://openalex.org/W2147674018","https://openalex.org/W2607135429","https://openalex.org/W2608864133","https://openalex.org/W2918466505","https://openalex.org/W2962701526","https://openalex.org/W2963649091","https://openalex.org/W2963944415","https://openalex.org/W2964061316","https://openalex.org/W2964097793","https://openalex.org/W2964246763","https://openalex.org/W2964311432","https://openalex.org/W3000299246","https://openalex.org/W3017446838","https://openalex.org/W3112650493","https://openalex.org/W3180026897","https://openalex.org/W4386254256","https://openalex.org/W4407634921","https://openalex.org/W6604583673"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"Abstract":[0],"The":[1,100],"local":[2,59,111,146],"h":[3,60,112,147],"-polynomial":[4,61,113,148],"was":[5],"introduced":[6],"by":[7],"Stanley":[8],"as":[9],"a":[10,15,23,105],"fundamental":[11],"enumerative":[12],"invariant":[13],"of":[14,22,66,79,89,114,134,144,149,154],"triangulation":[16,83,133],"$$\\Delta$$":[17,47,70,115,125],"<mml:math":[18,41,48,71,85,116,126,136],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[19,42,49,72,86,117,127,137],"<mml:mi>\u0394</mml:mi>":[20,50,73,118,128],"</mml:math>":[21,44,51,74,88,119,129,139],"simplex.":[24,91],"This":[25,54],"polynomial":[26],"is":[27,36,52,75,98,122,130,157],"known":[28],"to":[29,38],"have":[30],"nonnegative":[31],"and":[32,35],"symmetric":[33],"coefficients":[34],"conjectured":[37],"be":[39],"$$\\gamma$$":[40],"<mml:mi>\u03b3</mml:mi>":[43],"-positive":[45],"when":[46,69,124],"flag.":[53],"paper":[55],"shows":[56],"that":[57],"the":[58,63,76,90,110,145,150,155],"has":[62],"stronger":[64],"property":[65],"being":[67],"real-rooted":[68],"barycentric":[77,152],"subdivision":[78,153],"an":[80],"arbitrary":[81],"geometric":[82],"$$\\Gamma$$":[84,135],"<mml:mi>\u0393</mml:mi>":[87,138],"An":[92],"analogous":[93],"result":[94],"for":[95,109],"edgewise":[96],"subdivisions":[97],"proven.":[99],"proofs":[101],"are":[102],"based":[103],"on":[104],"new":[106],"combinatorial":[107,142],"formula":[108],",":[120],"which":[121],"valid":[123],"any":[131],"uniform":[132],".":[140],"A":[141],"interpretation":[143],"second":[151],"simplex":[156],"deduced.":[158]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}