{"id":"https://openalex.org/W1703437302","doi":"https://doi.org/10.1090/mcom/3098","title":"Searching for a counterexample to Kurepa\u2019s conjecture","display_name":"Searching for a counterexample to Kurepa\u2019s conjecture","publication_year":2015,"publication_date":"2015-08-28","ids":{"openalex":"https://openalex.org/W1703437302","doi":"https://doi.org/10.1090/mcom/3098","mag":"1703437302"},"language":"lv","primary_location":{"id":"doi:10.1090/mcom/3098","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3098","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1409.0800","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015263189","display_name":"Vladica Andreji\u0107","orcid":"https://orcid.org/0000-0003-3288-1845"},"institutions":[{"id":"https://openalex.org/I4068193","display_name":"University of Belgrade","ror":"https://ror.org/02qsmb048","country_code":"RS","type":"education","lineage":["https://openalex.org/I4068193"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Vladica Andreji\u0107","raw_affiliation_strings":["Faculty of Mathematics, University of Belgrade, Belgrade, Serbia#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, University of Belgrade, Belgrade, Serbia#TAB#","institution_ids":["https://openalex.org/I4068193"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019077826","display_name":"Milos Tatarevic","orcid":null},"institutions":[{"id":"https://openalex.org/I2802536887","display_name":"College of Alameda","ror":"https://ror.org/00vaf6k96","country_code":"US","type":"education","lineage":["https://openalex.org/I2802536887","https://openalex.org/I4210142450"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Milos Tatarevic","raw_affiliation_strings":["Alameda, California 94501"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Alameda, California 94501","institution_ids":["https://openalex.org/I2802536887"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5251,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.80732575,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"85","issue":"302","first_page":"3061","last_page":"3068"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9965999722480774,"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":0.9965999722480774,"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":0.9940000176429749,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9907000064849854,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.9706188440322876},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.8419607281684875},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8229063153266907},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.7363845109939575},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6199374198913574},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4453434348106384},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.41057509183883667},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21914276480674744}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.9706188440322876},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8419607281684875},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8229063153266907},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.7363845109939575},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6199374198913574},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4453434348106384},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.41057509183883667},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21914276480674744}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/mcom/3098","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3098","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1409.0800","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1409.0800","pdf_url":"https://arxiv.org/pdf/1409.0800","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"pmh:oai:CiteSeerX.psu:10.1.1.742.758","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.742.758","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1409.0800.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1409.0800","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1409.0800","pdf_url":"https://arxiv.org/pdf/1409.0800","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1555475515","https://openalex.org/W1632853461","https://openalex.org/W2004814164","https://openalex.org/W2037753389","https://openalex.org/W2041816918","https://openalex.org/W2065947172","https://openalex.org/W2124042897","https://openalex.org/W2126209209","https://openalex.org/W2146351362","https://openalex.org/W2333065485","https://openalex.org/W2914624816","https://openalex.org/W2962806999","https://openalex.org/W4206503652","https://openalex.org/W4237773356","https://openalex.org/W4293845860","https://openalex.org/W4302383489"],"related_works":["https://openalex.org/W4240581084","https://openalex.org/W2952569802","https://openalex.org/W4309222106","https://openalex.org/W4309876072","https://openalex.org/W2012590989","https://openalex.org/W4297939726","https://openalex.org/W2049141591","https://openalex.org/W4385681624","https://openalex.org/W2950489642","https://openalex.org/W1734188852"],"abstract_inverted_index":{"Kurepa\u2019s":[0,132],"conjecture":[1,84],"states":[2],"that":[3,21,242,286],"there":[4,268],"is":[5],"no":[6],"odd":[7,271],"prime":[8,272],"<inline-formula":[9,23,87,137,246,273,287],"content-type=\"math/mathml\">":[10,24,88,138,247,274,288],"<mml:math":[11,25,89,139,248,275,289],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[12,26,90,140,249,276,290],"alttext=\"p\">":[13,277],"<mml:semantics>":[14,44,96,175,255,278,298],"<mml:mi>p</mml:mi>":[15,47,61,98,279,300,308],"<mml:annotation":[16,70,108,231,263,280,310],"encoding=\"application/x-tex\">p</mml:annotation>":[17,281],"</mml:semantics>":[18,73,110,236,265,282,314],"</mml:math>":[19,74,111,237,266,283,315],"</inline-formula>":[20,75,112,238,267,284,316],"divides":[22],"alttext=\"factorial":[27,141],"p":[28,39],"equals":[29,146],"0":[30,148],"factorial":[31,34,134,149,157,171,293],"plus":[32,35,37,154,162,164],"1":[33,41,156,169],"midline-horizontal-ellipsis":[36,163],"left-parenthesis":[38,147,155,165,166],"minus":[40,168],"right-parenthesis":[42,150,158,170,172],"factorial\">":[43],"<mml:mrow>":[45,97,176,256,299],"<mml:mo>!</mml:mo>":[46,50,53,68,178,189,199,221,305],"<mml:mo>=</mml:mo>":[48,185],"<mml:mn>0</mml:mn>":[49,188],"<mml:mo>+</mml:mo>":[51,54,58,195,205,209],"<mml:mn>1</mml:mn>":[52,65,198,218,257],"<mml:mo>":[55,62,206,215,301],"\u22ef":[56,207],"</mml:mo>":[57,64,208,217,303],"<mml:mo":[59,66,186,191,196,201,210,212,219,223],"stretchy=\"false\">(</mml:mo>":[60,187,197,211,213],"\u2212":[63,216],"stretchy=\"false\">)</mml:mo>":[67,192,202,220,224],"</mml:mrow>":[69,105,107,182,228,230,262,309],"encoding=\"application/x-tex\">!p=0!+1!+\\cdots":[71],"+(p-1)!</mml:annotation>":[72],".":[76,113,317],"We":[77,114],"search":[78],"for":[79,85,243],"a":[80],"counterexample":[81],"to":[82],"this":[83],"all":[86,244],"alttext=\"p":[91,291],"greater-than":[92,251,253],"2":[93],"Superscript":[94,142,151,159,173,294],"34\">":[95],"<mml:mo>&gt;</mml:mo>":[99,258,260],"<mml:msup>":[100,177,190,200,222,304],"<mml:mn>2</mml:mn>":[101],"<mml:mrow":[102,179,225],"class=\"MJX-TeXAtom-ORD\">":[103,180,226],"<mml:mn>34</mml:mn>":[104],"</mml:msup>":[106,183,194,204,229,307],"encoding=\"application/x-tex\">p&gt;2^{34}</mml:annotation>":[109],"introduce":[115],"new":[116],"optimization":[117],"techniques":[118],"and":[119,240],"perform":[120],"the":[121,130],"computation":[122],"using":[123],"graphics":[124],"processing":[125],"units.":[126],"Additionally,":[127],"we":[128],"consider":[129],"generalized":[131],"left":[133],"given":[135],"by":[136],"k":[143,152,160,252,295],"Baseline":[144,153,161,296],"n":[145,167],"k\">":[174],"<mml:mi>k</mml:mi>":[181,193,203,227,259,306],"<mml:mi>n</mml:mi>":[184,214],"encoding=\"application/x-tex\">!^{k}n=(0!)^k":[232],"+(1!)^k":[233],"+\\cdots":[234],"+((n-1)!)^{k}</mml:annotation>":[235],",":[239],"show":[241],"integers":[245],"alttext=\"1":[250],"100\">":[254],"<mml:mn>100</mml:mn>":[261],"encoding=\"application/x-tex\">1&gt;k&gt;100</mml:annotation>":[264],"exists":[269],"an":[270],"such":[285],"bar":[292],"p\">":[297],"\u2223":[302],"encoding=\"application/x-tex\">p\\mid":[311],"!^k":[312],"p</mml:annotation>":[313]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2016-06-24T00:00:00"}
