{"id":"https://openalex.org/W2104796309","doi":"https://doi.org/10.37236/243","title":"A Short Proof, Based on Mixed Volumes, of Liggett's Theorem on the Convolution of Ultra-Logconcave Sequences","display_name":"A Short Proof, Based on Mixed Volumes, of Liggett's Theorem on the Convolution of Ultra-Logconcave Sequences","publication_year":2009,"publication_date":"2009-02-13","ids":{"openalex":"https://openalex.org/W2104796309","doi":"https://doi.org/10.37236/243","mag":"2104796309"},"language":"en","primary_location":{"id":"doi:10.37236/243","is_oa":true,"landing_page_url":"https://doi.org/10.37236/243","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1n5/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/v16i1n5/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022317936","display_name":"Leonid Gurvits","orcid":"https://orcid.org/0000-0002-0694-2459"},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Leonid Gurvits","raw_affiliation_strings":["Los Alamos National Laboratory"],"affiliations":[{"raw_affiliation_string":"Los Alamos National Laboratory","institution_ids":["https://openalex.org/I1343871089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5022317936"],"corresponding_institution_ids":["https://openalex.org/I1343871089"],"apc_list":null,"apc_paid":null,"fwci":2.3865,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.87908046,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"16","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9947999715805054,"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/mathematics","display_name":"Mathematics","score":0.8456571102142334},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.7243130207061768},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6345919370651245},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5719970464706421},{"id":"https://openalex.org/keywords/volume","display_name":"Volume (thermodynamics)","score":0.5429770946502686},{"id":"https://openalex.org/keywords/elementary-proof","display_name":"Elementary proof","score":0.4727124869823456},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35199272632598877},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18487930297851562},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08988520503044128},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06529629230499268}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8456571102142334},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.7243130207061768},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6345919370651245},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5719970464706421},{"id":"https://openalex.org/C20556612","wikidata":"https://www.wikidata.org/wiki/Q4469374","display_name":"Volume (thermodynamics)","level":2,"score":0.5429770946502686},{"id":"https://openalex.org/C2777478746","wikidata":"https://www.wikidata.org/wiki/Q5358910","display_name":"Elementary proof","level":2,"score":0.4727124869823456},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35199272632598877},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18487930297851562},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08988520503044128},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06529629230499268},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/243","is_oa":true,"landing_page_url":"https://doi.org/10.37236/243","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1n5/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:10.37236/243","is_oa":true,"landing_page_url":"https://doi.org/10.37236/243","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1n5/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":[{"id":"https://openalex.org/G5600677258","display_name":null,"funder_award_id":"U.S. DOE","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320337547","display_name":"Laboratory Directed Research and Development","ror":"https://ror.org/01e41cf67"},{"id":"https://openalex.org/F4320338304","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2104796309.pdf","grobid_xml":"https://content.openalex.org/works/W2104796309.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1883732049","https://openalex.org/W2022377411","https://openalex.org/W2056409716","https://openalex.org/W4213103933","https://openalex.org/W6819702625"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W2074376650","https://openalex.org/W3086542228","https://openalex.org/W2017331178","https://openalex.org/W2075243440","https://openalex.org/W2317836891","https://openalex.org/W2976797620","https://openalex.org/W2073495840","https://openalex.org/W2907358715","https://openalex.org/W2013984500"],"abstract_inverted_index":{"R.":[0],"Pemantle":[1],"conjectured,":[2],"and":[3],"T.M.":[4],"Liggett":[5],"proved":[6],"in":[7],"1997,":[8],"that":[9],"the":[10,31],"convolution":[11],"of":[12,34],"two":[13],"ultra-logconcave":[14],"is":[15,19],"ultra-logconcave.":[16],"Liggett's":[17],"proof":[18],"elementary":[20],"but":[21],"long.":[22],"We":[23],"present":[24],"here":[25],"a":[26],"short":[27],"proof,":[28],"based":[29],"on":[30],"mixed":[32],"volume":[33],"convex":[35],"sets.":[36]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-13T16:22:10.518609","created_date":"2025-10-10T00:00:00"}