{"id":"https://openalex.org/W3012810501","doi":"https://doi.org/10.37236/9456","title":"On the Intersection Distribution of Degree Three Polynomials and Related Topics","display_name":"On the Intersection Distribution of Degree Three Polynomials and Related Topics","publication_year":2021,"publication_date":"2021-06-18","ids":{"openalex":"https://openalex.org/W3012810501","doi":"https://doi.org/10.37236/9456","mag":"3012810501"},"language":"en","primary_location":{"id":"doi:10.37236/9456","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9456","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i2p46/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":"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":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i2p46/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060340286","display_name":"Gohar Kyureghyan","orcid":"https://orcid.org/0000-0003-0485-5500"},"institutions":[{"id":"https://openalex.org/I4210120266","display_name":"Czech Academy of Sciences, Institute of Mathematics","ror":"https://ror.org/02tv1yf50","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210120266"]},{"id":"https://openalex.org/I4665924","display_name":"University of Rostock","ror":"https://ror.org/03zdwsf69","country_code":"DE","type":"education","lineage":["https://openalex.org/I4665924"]}],"countries":["CZ","DE"],"is_corresponding":true,"raw_author_name":"Gohar Kyureghyan","raw_affiliation_strings":["Institute of Mathematics, University of Rostock","University of  Rostock"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Rostock","institution_ids":["https://openalex.org/I4665924","https://openalex.org/I4210120266"]},{"raw_affiliation_string":"University of  Rostock","institution_ids":["https://openalex.org/I4665924"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010168954","display_name":"Shuxing Li","orcid":"https://orcid.org/0000-0002-3405-3392"},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Shuxing Li","raw_affiliation_strings":["Department of Mathematics, Simon Fraser University","[Simon Fraser University]"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Simon Fraser University","institution_ids":["https://openalex.org/I18014758"]},{"raw_affiliation_string":"[Simon Fraser University]","institution_ids":["https://openalex.org/I18014758"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013787536","display_name":"Alexander Pott","orcid":"https://orcid.org/0000-0002-1125-1003"},"institutions":[{"id":"https://openalex.org/I95793202","display_name":"Otto-von-Guericke University Magdeburg","ror":"https://ror.org/00ggpsq73","country_code":"DE","type":"education","lineage":["https://openalex.org/I95793202"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Alexander Pott","raw_affiliation_strings":["Institute of Algebra and Geometry, Faculty of Mathematics, Otto von Guericke University Magdeburg","Otto-von-Guericke-University, Magdeburg"],"affiliations":[{"raw_affiliation_string":"Institute of Algebra and Geometry, Faculty of Mathematics, Otto von Guericke University Magdeburg","institution_ids":["https://openalex.org/I95793202"]},{"raw_affiliation_string":"Otto-von-Guericke-University, Magdeburg","institution_ids":["https://openalex.org/I95793202"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5060340286"],"corresponding_institution_ids":["https://openalex.org/I4210120266","https://openalex.org/I4665924"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.00517456,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"28","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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":1.0,"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":0.9987000226974487,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9984999895095825,"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/monomial","display_name":"Monomial","score":0.8498634099960327},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7040444612503052},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6934411525726318},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6708420515060425},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6382346153259277},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.6376503705978394},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.636136531829834},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.5865408778190613},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5461961627006531},{"id":"https://openalex.org/keywords/complete-intersection","display_name":"Complete intersection","score":0.5384352803230286},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.4745798110961914},{"id":"https://openalex.org/keywords/affine-space","display_name":"Affine space","score":0.4306640625},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.42208072543144226},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.359003484249115},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.323827862739563},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13665559887886047},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12427881360054016},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0646248459815979}],"concepts":[{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.8498634099960327},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7040444612503052},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6934411525726318},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6708420515060425},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6382346153259277},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6376503705978394},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.636136531829834},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.5865408778190613},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5461961627006531},{"id":"https://openalex.org/C37253","wikidata":"https://www.wikidata.org/wiki/Q5156502","display_name":"Complete intersection","level":2,"score":0.5384352803230286},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.4745798110961914},{"id":"https://openalex.org/C173110770","wikidata":"https://www.wikidata.org/wiki/Q382698","display_name":"Affine space","level":3,"score":0.4306640625},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.42208072543144226},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.359003484249115},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.323827862739563},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13665559887886047},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12427881360054016},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0646248459815979},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/9456","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9456","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i2p46/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":"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"},{"id":"pmh:oai:arXiv.org:2003.10040","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.10040","pdf_url":"https://arxiv.org/pdf/2003.10040","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3012810501","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2003.10040.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2003.10040","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2003.10040","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.37236/9456","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9456","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i2p46/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":"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":[{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"},{"id":"https://openalex.org/F4320310984","display_name":"Pacific Institute for the Mathematical Sciences","ror":"https://ror.org/04w49dw51"},{"id":"https://openalex.org/F4320327736","display_name":"Universit\u00e4t Rostock","ror":"https://ror.org/03zdwsf69"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3012810501.pdf","grobid_xml":"https://content.openalex.org/works/W3012810501.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W114491584","https://openalex.org/W1559387471","https://openalex.org/W1587687098","https://openalex.org/W1961402164","https://openalex.org/W1997424790","https://openalex.org/W2045794269","https://openalex.org/W2052031636","https://openalex.org/W2059370662","https://openalex.org/W2064186082","https://openalex.org/W2065619397","https://openalex.org/W2082143349","https://openalex.org/W2083468009","https://openalex.org/W2086996205","https://openalex.org/W2089277105","https://openalex.org/W2099197486","https://openalex.org/W2105985720","https://openalex.org/W2124113125","https://openalex.org/W2129953187","https://openalex.org/W2141189030","https://openalex.org/W2292469948","https://openalex.org/W2334224849","https://openalex.org/W2489161884","https://openalex.org/W2564173521","https://openalex.org/W2922182580","https://openalex.org/W2963746184","https://openalex.org/W3010894784","https://openalex.org/W3012378409","https://openalex.org/W3016114799","https://openalex.org/W3032938687","https://openalex.org/W6633379478","https://openalex.org/W6640935892","https://openalex.org/W6665304244"],"related_works":["https://openalex.org/W3173216433","https://openalex.org/W2593590535","https://openalex.org/W3014149009","https://openalex.org/W3103665618","https://openalex.org/W2953704311","https://openalex.org/W2078152650","https://openalex.org/W2292474944","https://openalex.org/W3037742570","https://openalex.org/W836282740","https://openalex.org/W2129153740","https://openalex.org/W2103774383","https://openalex.org/W2962841068","https://openalex.org/W114782766","https://openalex.org/W2463920666","https://openalex.org/W2327940002","https://openalex.org/W1490566753","https://openalex.org/W2949567306","https://openalex.org/W3106110412","https://openalex.org/W2949581420","https://openalex.org/W2009550926"],"abstract_inverted_index":{"The":[0,39,166],"intersection":[1,40,50,91,110,135,158],"distribution":[2,41,92,111,136],"of":[3,30,33,55,73,142,156,160,172,184],"a":[4,31,80,148],"polynomial":[5],"$f$":[6,56],"over":[7,117],"finite":[8],"field":[9],"$\\mathbb{F}_q$":[10,118],"was":[11],"recently":[12],"proposed":[13],"by":[14,96],"Li":[15],"and":[16,20,57,107,123,147,177],"Pott":[17],"[\\emph{Finite":[18],"Fields":[19],"Their":[21],"Applications,":[22],"66":[23],"(2020)}],":[24],"which":[25,47,87],"concerns":[26],"the":[27,49,53,58,61,69,89,103,109,133,157,170,178],"collective":[28],"behaviour":[29],"collection":[32],"polynomials":[34,86,116,163],"$\\{f(x)+cx":[35],"\\mid":[36],"c":[37],"\\in\\mathbb{F}_q\\}$.":[38],"has":[42],"an":[43],"underlying":[44],"geometric":[45],"interpretation,":[46],"indicates":[48],"pattern":[51],"between":[52],"graph":[54],"lines":[59],"in":[60,79,187],"affine":[62,188],"plane":[63],"$AG(2,q)$.":[64],"When":[65],"$q$":[66,120],"is":[67,150,169],"even,":[68],"long-standing":[70],"open":[71],"problem":[72],"classifying":[74,84],"o-polynomials":[75],"can":[76],"be":[77],"rephrased":[78],"simple":[81],"way,":[82],"namely,":[83],"all":[85,113,130],"have":[88],"same":[90,134],"as":[93,137],"$x^2$.":[94],"Inspired":[95],"this":[97],"connection,":[98],"we":[99,126],"proceed":[100],"to":[101,128],"consider":[102],"next":[104],"simplest":[105],"case":[106],"derive":[108],"for":[112],"degree":[114,161],"three":[115,162],"with":[119,190],"both":[121],"odd":[122],"even.":[124],"Moreover,":[125],"initiate":[127],"classify":[129],"monomials":[131,144],"having":[132],"$x^3$,":[138],"where":[139],"some":[140],"characterizations":[141],"such":[143],"are":[145,164],"obtained":[146],"conjecture":[149],"proposed.":[151],"In":[152],"addition,":[153],"two":[154],"applications":[155],"distributions":[159],"presented.":[165],"first":[167],"one":[168,180],"construction":[171],"nonisomorphic":[173],"Steiner":[174],"triple":[175],"systems":[176],"second":[179],"produces":[181],"infinite":[182],"families":[183],"Kakeya":[185],"sets":[186],"planes":[189],"previously":[191],"unknown":[192],"sizes.":[193]},"counts_by_year":[{"year":2020,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}