{"id":"https://openalex.org/W3138442000","doi":"https://doi.org/10.1137/20m1369439","title":"Improved Bounds on Sizes of Generalized Caps in $AG(n,q)$","display_name":"Improved Bounds on Sizes of Generalized Caps in $AG(n,q)$","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3138442000","doi":"https://doi.org/10.1137/20m1369439","mag":"3138442000"},"language":"en","primary_location":{"id":"doi:10.1137/20m1369439","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1369439","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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/A5054251227","display_name":"Michael Tait","orcid":"https://orcid.org/0000-0003-3695-6883"},"institutions":[{"id":"https://openalex.org/I7863295","display_name":"Villanova University","ror":"https://ror.org/02g7kd627","country_code":"US","type":"education","lineage":["https://openalex.org/I7863295"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Michael Tait","raw_affiliation_strings":["Villanova University, Department of Mathematics and Statistics, Villanova, PA 19085,"],"raw_orcid":"https://orcid.org/0000-0003-3695-6883","affiliations":[{"raw_affiliation_string":"Villanova University, Department of Mathematics and Statistics, Villanova, PA 19085,","institution_ids":["https://openalex.org/I7863295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029965211","display_name":"Robert Won","orcid":"https://orcid.org/0000-0002-9965-3196"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert Won","raw_affiliation_strings":["University of Washington, Department of Mathematics, Seattle, WA 98195,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Washington, Department of Mathematics, Seattle, WA 98195,","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5054251227"],"corresponding_institution_ids":["https://openalex.org/I7863295"],"apc_list":null,"apc_paid":null,"fwci":1.1199,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.8177871,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"35","issue":"1","first_page":"521","last_page":"531"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9994000196456909,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7530495524406433},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6623408198356628},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4487076997756958}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7530495524406433},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6623408198356628},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4487076997756958}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/20m1369439","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1369439","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2120803139","display_name":null,"funder_award_id":"2011553","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6323940620","display_name":null,"funder_award_id":"DMS-2011553","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1513028911","https://openalex.org/W1533675320","https://openalex.org/W1569552448","https://openalex.org/W1573651432","https://openalex.org/W1587687098","https://openalex.org/W1629301835","https://openalex.org/W1979562204","https://openalex.org/W1990102738","https://openalex.org/W1999359691","https://openalex.org/W2015568452","https://openalex.org/W2072865951","https://openalex.org/W2088269690","https://openalex.org/W2114487569","https://openalex.org/W2117908084","https://openalex.org/W2118153390","https://openalex.org/W2559529531","https://openalex.org/W2765523696","https://openalex.org/W2839002320","https://openalex.org/W2890935468","https://openalex.org/W2953863565","https://openalex.org/W2962911461","https://openalex.org/W2963019803","https://openalex.org/W2963580746","https://openalex.org/W2963631653","https://openalex.org/W3105325455","https://openalex.org/W3122194804"],"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/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"An":[0],"$m$-general":[1,39],"set":[2,7,23,40],"in":[3,18,41],"$AG(n,q)$":[4],"is":[5,17,24],"a":[6,27,53,57],"of":[8,14,37],"points":[9],"such":[10],"that":[11],"any":[12],"subset":[13],"size":[15,36],"$m$":[16],"general":[19],"position.":[20],"A":[21],"3-general":[22],"often":[25],"called":[26],"capset.":[28],"In":[29],"this":[30],"paper,":[31],"we":[32,51],"study":[33],"the":[34],"maximum":[35],"an":[38],"$AG(n,q)$,":[42],"significantly":[43],"improving":[44],"previous":[45],"results.":[46],"When":[47],"$m=4$":[48],"and":[49],"$q=2$,":[50],"give":[52],"precise":[54],"estimate,":[55],"solving":[56],"problem":[58],"raised":[59],"by":[60],"Bennett.":[61]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}