{"id":"https://openalex.org/W2108616329","doi":"https://doi.org/10.1017/s0963548311000277","title":"On Sumsets of Convex Sets","display_name":"On Sumsets of Convex Sets","publication_year":2011,"publication_date":"2011-07-07","ids":{"openalex":"https://openalex.org/W2108616329","doi":"https://doi.org/10.1017/s0963548311000277","mag":"2108616329"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548311000277","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548311000277","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040639904","display_name":"Tomasz Schoen","orcid":"https://orcid.org/0000-0002-9427-3127"},"institutions":[{"id":"https://openalex.org/I59411706","display_name":"Adam Mickiewicz University in Pozna\u0144","ror":"https://ror.org/04g6bbq64","country_code":"PL","type":"education","lineage":["https://openalex.org/I59411706"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"TOMASZ SCHOEN","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Pozna\u0144, Poland (e-mail:","Faculty of mathematics and computer science, adam mickiewicz university, umultowska 87, 61-614 pozna\u0144, poland (e-mail: schoen@amu.edu.pl)#TAB#"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Pozna\u0144, Poland (e-mail:","institution_ids":["https://openalex.org/I59411706"]},{"raw_affiliation_string":"Faculty of mathematics and computer science, adam mickiewicz university, umultowska 87, 61-614 pozna\u0144, poland (e-mail: schoen@amu.edu.pl)#TAB#","institution_ids":["https://openalex.org/I59411706"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071151408","display_name":"Ilya D. Shkredov","orcid":"https://orcid.org/0000-0002-6445-8390"},"institutions":[{"id":"https://openalex.org/I2801160905","display_name":"Steklov Mathematical Institute","ror":"https://ror.org/03zeg8w71","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I2801160905","https://openalex.org/I4210124601"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"ILYA D. SHKREDOV","raw_affiliation_strings":["Division of Algebra and Number Theory, Steklov Mathematical Institute, ul. Gubkina, 8, Moscow, 119991Russia (e-mail:","Division of algebra and number theory, steklov mathematical institute, ul. gubkina, 8, moscow, 119991russia (e-mail: ilya.shkredov@gmail.com)#TAB#"],"affiliations":[{"raw_affiliation_string":"Division of Algebra and Number Theory, Steklov Mathematical Institute, ul. Gubkina, 8, Moscow, 119991Russia (e-mail:","institution_ids":["https://openalex.org/I2801160905"]},{"raw_affiliation_string":"Division of algebra and number theory, steklov mathematical institute, ul. gubkina, 8, moscow, 119991russia (e-mail: ilya.shkredov@gmail.com)#TAB#","institution_ids":["https://openalex.org/I2801160905"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5040639904"],"corresponding_institution_ids":["https://openalex.org/I59411706"],"apc_list":null,"apc_paid":null,"fwci":7.7111,"has_fulltext":false,"cited_by_count":58,"citation_normalized_percentile":{"value":0.98633257,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"20","issue":"5","first_page":"793","last_page":"798"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9993000030517578,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9993000030517578,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9973000288009644,"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/combinatorics","display_name":"Combinatorics","score":0.7184560894966125},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6553909182548523},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5929407477378845},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.5503154397010803},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5237017869949341},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.22468483448028564},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19199270009994507},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06660208106040955}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7184560894966125},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6553909182548523},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5929407477378845},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.5503154397010803},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5237017869949341},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.22468483448028564},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19199270009994507},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06660208106040955},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0963548311000277","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548311000277","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W139290095","https://openalex.org/W1998666916","https://openalex.org/W2010812191","https://openalex.org/W2013805017","https://openalex.org/W2023794140","https://openalex.org/W2039925482","https://openalex.org/W2075616478","https://openalex.org/W2086551468","https://openalex.org/W2086861401","https://openalex.org/W2103381743","https://openalex.org/W2118172901","https://openalex.org/W2166961358","https://openalex.org/W2914100914","https://openalex.org/W3100139723","https://openalex.org/W3105850305","https://openalex.org/W6605647162"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W4288324104","https://openalex.org/W2951573408","https://openalex.org/W4238664286","https://openalex.org/W2941078816","https://openalex.org/W72541825"],"abstract_inverted_index":{"A":[0,4,49,52,54,59,65],"set":[1],"of":[2],"reals":[3],"=":[5],"{":[6],"a":[7,12,19,23,26,29],"1":[8],",.":[9],".":[10,35],".,":[11],"n":[13],"}":[14],"is":[15],"called":[16],"convex":[17,48],"if":[18],"i":[20,24,27,30,34],"+1":[21],"\u2212":[22,28,53],">":[25,45],"\u22121":[31],"for":[32,42],"all":[33],"We":[36],"prove,":[37],"among":[38],"other":[39],"results,":[40],"that":[41],"some":[43],"c":[44,57],"0":[46],"every":[47],"satisfies":[50],"|":[51,55,58,60,64],"\u2265":[56],"8/5":[61],"log":[62],"\u22122/5":[63],"|.":[66]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}