{"id":"https://openalex.org/W1541755919","doi":"https://doi.org/10.37236/1186","title":"The prime power conjecture is true for $n < 2{,}000{,}000$","display_name":"The prime power conjecture is true for $n < 2{,}000{,}000$","publication_year":1994,"publication_date":"1994-08-24","ids":{"openalex":"https://openalex.org/W1541755919","doi":"https://doi.org/10.37236/1186","mag":"1541755919"},"language":"en","primary_location":{"id":"doi:10.37236/1186","is_oa":false,"landing_page_url":"https://doi.org/10.37236/1186","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":false,"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":null,"license_id":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085783796","display_name":"Daniel M. Gordon","orcid":"https://orcid.org/0000-0003-4373-3637"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Daniel M. Gordon","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5085783796"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.04631914,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"1","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9991000294685364,"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/T11130","display_name":"Coding theory and cryptography","score":0.9559999704360962,"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/T11215","display_name":"Chronic Myeloid Leukemia Treatments","score":0.9319000244140625,"subfield":{"id":"https://openalex.org/subfields/2720","display_name":"Hematology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8967868685722351},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.818558394908905},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.7849292159080505},{"id":"https://openalex.org/keywords/prime-power","display_name":"Prime power","score":0.7460159063339233},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.678429126739502},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.657467782497406},{"id":"https://openalex.org/keywords/cyclic-group","display_name":"Cyclic group","score":0.5818769931793213},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5372422337532043},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4137660562992096}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8967868685722351},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.818558394908905},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.7849292159080505},{"id":"https://openalex.org/C174072685","wikidata":"https://www.wikidata.org/wiki/Q1667469","display_name":"Prime power","level":3,"score":0.7460159063339233},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.678429126739502},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.657467782497406},{"id":"https://openalex.org/C20725272","wikidata":"https://www.wikidata.org/wiki/Q245462","display_name":"Cyclic group","level":3,"score":0.5818769931793213},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5372422337532043},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4137660562992096},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/1186","is_oa":false,"landing_page_url":"https://doi.org/10.37236/1186","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":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W28083287","https://openalex.org/W122098849","https://openalex.org/W1987701799","https://openalex.org/W1992550814","https://openalex.org/W2035701841","https://openalex.org/W2110278130"],"related_works":["https://openalex.org/W4320035778","https://openalex.org/W2070845140","https://openalex.org/W2543275399","https://openalex.org/W4366526577","https://openalex.org/W2318047582","https://openalex.org/W1998402533","https://openalex.org/W2069443110","https://openalex.org/W2292792029","https://openalex.org/W2085587817","https://openalex.org/W1992434689"],"abstract_inverted_index":{"The":[0],"Prime":[1],"Power":[2],"Conjecture":[3],"(PPC)":[4],"states":[5],"that":[6],"abelian":[7],"planar":[8],"difference":[9,28],"sets":[10,29],"of":[11,52],"order":[12],"$n$":[13,17],"exist":[14],"only":[15],"for":[16,26,30,41],"a":[18],"prime":[19],"power.":[20],"Evans":[21],"and":[22],"Mann":[23],"verified":[24],"this":[25,35],"cyclic":[27],"$n":[31,42],"\\leq":[32,43],"1600$.":[33],"In":[34],"paper":[36],"we":[37],"verify":[38],"the":[39,50],"PPC":[40],"2{,}000{,}000$,":[44],"using":[45],"many":[46],"necessary":[47],"conditions":[48],"on":[49],"group":[51],"multipliers.":[53]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}