{"id":"https://openalex.org/W2963920124","doi":"https://doi.org/10.1137/17m1146099","title":"Finite Field Kakeya and Nikodym Sets in Three Dimensions","display_name":"Finite Field Kakeya and Nikodym Sets in Three Dimensions","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2963920124","doi":"https://doi.org/10.1137/17m1146099","mag":"2963920124"},"language":"en","primary_location":{"id":"doi:10.1137/17m1146099","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1146099","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/A5048694724","display_name":"Ben Lund","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ben Lund","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020540233","display_name":"Shubhangi Saraf","orcid":"https://orcid.org/0009-0005-0874-2978"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shubhangi Saraf","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5102961868","display_name":"Charles Wolf","orcid":"https://orcid.org/0000-0001-5828-6740"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Charles Wolf","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5048694724"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6104,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.83476253,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"32","issue":"4","first_page":"2836","last_page":"2849"},"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":0.9983000159263611,"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":0.9983000159263611,"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.9955999851226807,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9836000204086304,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.8652075529098511},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.8259235620498657},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6806147694587708},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5382781624794006},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5365279912948608},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.48681017756462097},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4823543429374695},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.45715636014938354},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1665184497833252},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07886779308319092},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0595088005065918}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8652075529098511},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8259235620498657},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6806147694587708},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5382781624794006},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5365279912948608},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.48681017756462097},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4823543429374695},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.45715636014938354},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1665184497833252},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07886779308319092},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0595088005065918},{"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:10.1137/17m1146099","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1146099","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/G3396274902","display_name":null,"funder_award_id":"CCF-1350572","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1535020102","https://openalex.org/W1997424790","https://openalex.org/W1998400388","https://openalex.org/W2016044354","https://openalex.org/W2019273286","https://openalex.org/W2055847334","https://openalex.org/W2060493211","https://openalex.org/W2062496697","https://openalex.org/W2144543987","https://openalex.org/W2334979462","https://openalex.org/W2963096774","https://openalex.org/W3124433407","https://openalex.org/W4254683461"],"related_works":["https://openalex.org/W3194471551","https://openalex.org/W4375956809","https://openalex.org/W1581373162","https://openalex.org/W2784911598","https://openalex.org/W4297950433","https://openalex.org/W4287023968","https://openalex.org/W4288279572","https://openalex.org/W1973978937","https://openalex.org/W4286909116","https://openalex.org/W2964302506"],"abstract_inverted_index":{"We":[0,15],"give":[1],"improved":[2],"lower":[3],"bounds":[4],"on":[5,21,47],"the":[6,22,28,48],"size":[7,49],"of":[8,25,30,34,50],"Kakeya":[9],"and":[10,38],"Nikodym":[11,52],"sets":[12],"over":[13],"$\\Bbb{F}_q^3$.":[14],"also":[16],"propose":[17],"a":[18,31,51],"natural":[19],"conjecture":[20,42],"minimum":[23],"number":[24],"points":[26],"in":[27,36],"union":[29],"not-too-flat":[32],"set":[33],"lines":[35],"$\\Bbb{F}_q^3$":[37],"show":[39],"that":[40],"this":[41],"implies":[43],"an":[44],"optimal":[45],"bound":[46],"set.":[53]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}