{"id":"https://openalex.org/W3000082363","doi":"https://doi.org/10.37236/1153","title":"An Ehrhart Series Formula For Reflexive Polytopes","display_name":"An Ehrhart Series Formula For Reflexive Polytopes","publication_year":2006,"publication_date":"2006-10-05","ids":{"openalex":"https://openalex.org/W3000082363","doi":"https://doi.org/10.37236/1153","mag":"3000082363"},"language":"en","primary_location":{"id":"doi:10.37236/1153","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1153","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1n15/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":null,"license_id":null,"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/v13i1n15/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055368173","display_name":"Benjamin Braun","orcid":"https://orcid.org/0000-0001-6636-8156"},"institutions":[{"id":"https://openalex.org/I204465549","display_name":"Washington University in St. Louis","ror":"https://ror.org/01yc7t268","country_code":"US","type":"education","lineage":["https://openalex.org/I204465549"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Benjamin Braun","raw_affiliation_strings":["Department of Mathematics Washington University, St. Louis, MO"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Washington University, St. Louis, MO","institution_ids":["https://openalex.org/I204465549"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5055368173"],"corresponding_institution_ids":["https://openalex.org/I204465549"],"apc_list":null,"apc_paid":null,"fwci":1.4067,"has_fulltext":true,"cited_by_count":38,"citation_normalized_percentile":{"value":0.81438721,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"13","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/T11428","display_name":"Advanced Mathematical Identities","score":0.9984999895095825,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/polytope","display_name":"Polytope","score":0.9184512495994568},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.8649940490722656},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7923688888549805},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7884928584098816},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5250556468963623},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.4826098680496216},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3712543845176697},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0706794261932373},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05722588300704956}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.9184512495994568},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.8649940490722656},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7923688888549805},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7884928584098816},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5250556468963623},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4826098680496216},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3712543845176697},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0706794261932373},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05722588300704956},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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":1,"locations":[{"id":"doi:10.37236/1153","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1153","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1n15/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":null,"license_id":null,"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:10.37236/1153","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1153","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1n15/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3000082363.pdf","grobid_xml":"https://content.openalex.org/works/W3000082363.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W135008847","https://openalex.org/W1537523458","https://openalex.org/W1796115931","https://openalex.org/W1980939657","https://openalex.org/W2914659449","https://openalex.org/W4243994785","https://openalex.org/W4301042554"],"related_works":["https://openalex.org/W2107784188","https://openalex.org/W4295332765","https://openalex.org/W2489571958","https://openalex.org/W1845479838","https://openalex.org/W4372320108","https://openalex.org/W2753535706","https://openalex.org/W2068573068","https://openalex.org/W2894444216","https://openalex.org/W2950516911","https://openalex.org/W2950982538"],"abstract_inverted_index":{"It":[0],"is":[1,24,48],"well":[2],"known":[3],"that":[4,22,44],"for":[5,33,35,38],"$P$":[6,47],"and":[7,37,50],"$Q$":[8,51],"lattice":[9],"polytopes,":[10],"the":[11,30,39],"Ehrhart":[12,31],"polynomial":[13],"of":[14],"$P\\times":[15],"Q$":[16,43],"satisfies":[17],"$L_{P\\times":[18],"Q}(t)=L_P(t)L_Q(t)$.":[19],"We":[20],"show":[21],"there":[23],"a":[25],"similar":[26],"multiplicative":[27],"relationship":[28],"between":[29],"series":[32],"$P$,":[34],"$Q$,":[36],"free":[40],"sum":[41],"$P\\oplus":[42],"holds":[45],"when":[46],"reflexive":[49],"contains":[52],"$0$":[53],"in":[54],"its":[55],"interior.":[56]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":16},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
