{"id":"https://openalex.org/W2963478098","doi":"https://doi.org/10.37236/7275","title":"Erd&amp;#337;s-Ginzburg-Ziv Constants by Avoiding Three-Term Arithmetic Progressions","display_name":"Erd&amp;#337;s-Ginzburg-Ziv Constants by Avoiding Three-Term Arithmetic Progressions","publication_year":2018,"publication_date":"2018-04-27","ids":{"openalex":"https://openalex.org/W2963478098","doi":"https://doi.org/10.37236/7275","mag":"2963478098"},"language":"en","primary_location":{"id":"doi:10.37236/7275","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7275","pdf_url":null,"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":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37236/7275","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112361944","display_name":"Jacob Fox","orcid":"https://orcid.org/0000-0002-0664-497X"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jacob Fox","raw_affiliation_strings":["Stanford University"],"affiliations":[{"raw_affiliation_string":"Stanford University","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069778690","display_name":"Lisa Sauermann","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lisa Sauermann","raw_affiliation_strings":["Stanford University"],"affiliations":[{"raw_affiliation_string":"Stanford University","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5112361944"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":5.6357,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.9691144,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"25","issue":"2","first_page":null,"last_page":null},"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":0.9988999962806702,"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":0.9988999962806702,"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/T10849","display_name":"Finite Group Theory Research","score":0.9889000058174133,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9550999999046326,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8233025074005127},{"id":"https://openalex.org/keywords/subsequence","display_name":"Subsequence","score":0.8194884061813354},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7840394973754883},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5863803625106812},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5724193453788757},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.5622288584709167},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.529859721660614},{"id":"https://openalex.org/keywords/arithmetic-progression","display_name":"Arithmetic progression","score":0.5278539657592773},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4560137391090393},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09861546754837036},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06913676857948303},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.05439910292625427}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8233025074005127},{"id":"https://openalex.org/C137877099","wikidata":"https://www.wikidata.org/wiki/Q1332977","display_name":"Subsequence","level":3,"score":0.8194884061813354},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7840394973754883},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5863803625106812},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5724193453788757},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5622288584709167},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.529859721660614},{"id":"https://openalex.org/C130498168","wikidata":"https://www.wikidata.org/wiki/Q170008","display_name":"Arithmetic progression","level":2,"score":0.5278539657592773},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4560137391090393},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09861546754837036},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06913676857948303},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.05439910292625427},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"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:10.37236/7275","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7275","pdf_url":null,"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"}],"best_oa_location":{"id":"doi:10.37236/7275","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7275","pdf_url":null,"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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4230102134","https://openalex.org/W2996768723","https://openalex.org/W4212895949","https://openalex.org/W4247866870","https://openalex.org/W2112772040","https://openalex.org/W3216774880","https://openalex.org/W2078387789","https://openalex.org/W2187658836","https://openalex.org/W4287997543","https://openalex.org/W2992962258"],"abstract_inverted_index":{"For":[0,33,92],"a":[1,27,34,49],"finite":[2],"abelian":[3],"group":[4],"$G$,":[5],"The":[6],"Erd\u0151s-Ginzburg-Ziv":[7],"constant":[8],"$\\mathfrak{s}(G)$":[9,61,80],"is":[10],"the":[11,40,43,86,93,103,115],"smallest":[12],"$s$":[13,19],"such":[14],"that":[15],"every":[16],"sequence":[17],"of":[18,24,30,42,46,83,90,108],"(not":[20],"necessarily":[21],"distinct)":[22],"elements":[23],"$G$":[25],"has":[26,70],"zero-sum":[28],"subsequence":[29],"length":[31],"$\\operatorname{exp}(G)$.":[32,91],"prime":[35,87],"$p$,":[36],"let":[37],"$r(\\mathbb{F}_p^n)$":[38,84,107],"denote":[39],"size":[41],"largest":[44],"subset":[45],"$\\mathbb{F}_p^n$":[47],"without":[48],"three-term":[50],"arithmetic":[51],"progression.":[52],"Although":[53],"similar":[54],"methods":[55],"have":[56],"been":[57,72],"used":[58],"to":[59],"study":[60],"and":[62,110],"$r(\\mathbb{F}_p^n)$,":[63],"no":[64],"direct":[65],"connection":[66],"between":[67],"these":[68],"quantities":[69],"previously":[71,116],"established.":[73],"We":[74],"give":[75],"an":[76],"upper":[77,104,119],"bound":[78],"for":[79,85,106,121],"in":[81],"terms":[82],"divisors":[88],"$p$":[89],"special":[94],"case":[95],"$G=\\mathbb{F}_p^n$,":[96],"we":[97],"prove":[98],"$\\mathfrak{s}(\\mathbb{F}_p^n)\\leq":[99],"2p\\cdot":[100],"r(\\mathbb{F}_p^n)$.":[101],"Using":[102],"bounds":[105,120],"Ellenberg":[109],"Gijswijt,":[111],"this":[112],"result":[113],"improves":[114],"best":[117],"known":[118],"$\\mathfrak{s}(\\mathbb{F}_p^n)$":[122],"given":[123],"by":[124],"Naslund.":[125]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
