{"id":"https://openalex.org/W564502725","doi":"https://doi.org/10.37236/5340","title":"Permutations Destroying Arithmetic Progressions in Finite Cyclic Groups","display_name":"Permutations Destroying Arithmetic Progressions in Finite Cyclic Groups","publication_year":2015,"publication_date":"2015-12-11","ids":{"openalex":"https://openalex.org/W564502725","doi":"https://doi.org/10.37236/5340","mag":"564502725"},"language":"en","primary_location":{"id":"doi:10.37236/5340","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5340","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i4p39/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":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i4p39/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012383867","display_name":"Peter Hegarty","orcid":"https://orcid.org/0000-0002-5487-4075"},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]},{"id":"https://openalex.org/I881427289","display_name":"University of Gothenburg","ror":"https://ror.org/01tm6cn81","country_code":"SE","type":"education","lineage":["https://openalex.org/I881427289"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Peter Hegarty","raw_affiliation_strings":["Chalmers University of Technology and University of Gothenburg","Chalmers University of Technology & University of Gothenburg"],"affiliations":[{"raw_affiliation_string":"Chalmers University of Technology and University of Gothenburg","institution_ids":["https://openalex.org/I66862912","https://openalex.org/I881427289"]},{"raw_affiliation_string":"Chalmers University of Technology & University of Gothenburg","institution_ids":["https://openalex.org/I66862912","https://openalex.org/I881427289"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049015414","display_name":"Anders Martinsson","orcid":null},"institutions":[{"id":"https://openalex.org/I881427289","display_name":"University of Gothenburg","ror":"https://ror.org/01tm6cn81","country_code":"SE","type":"education","lineage":["https://openalex.org/I881427289"]},{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Anders Martinsson","raw_affiliation_strings":["Chalmers University of Technology and University of Gothenburg","Chalmers University of Technology & University of Gothenburg"],"affiliations":[{"raw_affiliation_string":"Chalmers University of Technology and University of Gothenburg","institution_ids":["https://openalex.org/I66862912","https://openalex.org/I881427289"]},{"raw_affiliation_string":"Chalmers University of Technology & University of Gothenburg","institution_ids":["https://openalex.org/I66862912","https://openalex.org/I881427289"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5012383867"],"corresponding_institution_ids":["https://openalex.org/I66862912","https://openalex.org/I881427289"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00291589,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":"4","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":0.9994000196456909,"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":0.9994000196456909,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9991999864578247,"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/T10849","display_name":"Finite Group Theory Research","score":0.9980999827384949,"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":0.8468505144119263},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8101819753646851},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.7666077613830566},{"id":"https://openalex.org/keywords/arithmetic-progression","display_name":"Arithmetic progression","score":0.6142624616622925},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.5792739391326904},{"id":"https://openalex.org/keywords/permutation-group","display_name":"Permutation group","score":0.5142459273338318},{"id":"https://openalex.org/keywords/cyclic-group","display_name":"Cyclic group","score":0.4732509255409241},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.43938836455345154},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4015001058578491},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0770060122013092}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8468505144119263},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8101819753646851},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.7666077613830566},{"id":"https://openalex.org/C130498168","wikidata":"https://www.wikidata.org/wiki/Q170008","display_name":"Arithmetic progression","level":2,"score":0.6142624616622925},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5792739391326904},{"id":"https://openalex.org/C92957085","wikidata":"https://www.wikidata.org/wiki/Q1412905","display_name":"Permutation group","level":3,"score":0.5142459273338318},{"id":"https://openalex.org/C20725272","wikidata":"https://www.wikidata.org/wiki/Q245462","display_name":"Cyclic group","level":3,"score":0.4732509255409241},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.43938836455345154},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4015001058578491},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0770060122013092},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/5340","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5340","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i4p39/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:research.chalmers.se:218523","is_oa":false,"landing_page_url":"https://research.chalmers.se/en/publication/218523","pdf_url":null,"source":{"id":"https://openalex.org/S4306402469","display_name":"Chalmers Research (Chalmers University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66862912","host_organization_name":"Chalmers University of Technology","host_organization_lineage":["https://openalex.org/I66862912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"doi:10.37236/5340","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5340","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i4p39/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":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W564502725.pdf","grobid_xml":"https://content.openalex.org/works/W564502725.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1005731694","https://openalex.org/W1520833852","https://openalex.org/W1956715345","https://openalex.org/W2085279685","https://openalex.org/W2117908084"],"related_works":["https://openalex.org/W4320035778","https://openalex.org/W2070845140","https://openalex.org/W209367526","https://openalex.org/W368092084","https://openalex.org/W2506973052","https://openalex.org/W2318047582","https://openalex.org/W4389139084","https://openalex.org/W4320165426","https://openalex.org/W4366206987","https://openalex.org/W1992434689"],"abstract_inverted_index":{"A":[0],"permutation":[1,63,93,115],"$\\pi$":[2],"of":[3,65,85,116],"an":[4,49],"abelian":[5],"group":[6],"$G$":[7],"is":[8,22,30,47],"said":[9],"to":[10],"destroy":[11],"arithmetic":[12],"progressions":[13],"(APs)":[14],"if,":[15],"whenever":[16],"$(a,":[17],"\\,":[18,20,34,36,44,72,74,76],"b,":[19,35],"c)$":[21],"a":[23,52,62,82,86,92,114],"non-trivial":[24],"3-term":[25],"AP":[26],"in":[27],"$G$,":[28],"that":[29,60,90,125],"$c-b=b-a$":[31],"and":[32],"$a,":[33],"c$":[37],"are":[38],"not":[39,48],"all":[40,68,96,119],"equal,":[41],"then":[42],"$(\\pi(a),":[43],"\\pi(b),":[45],"\\pi(c))$":[46],"AP.":[50],"In":[51],"paper":[53],"from":[54],"2004,":[55],"the":[56],"first":[57],"author":[58],"conjectured":[59],"such":[61,91,113,124],"exists":[64,94],"$\\mathbb{Z}_n$,":[66],"for":[67,95,100,118],"$n":[69,97],"\\not\\in":[70],"\\{2,":[71],"3,":[73],"5,":[75],"7\\}$.":[77],"Here":[78],"we":[79],"prove,":[80],"as":[81],"special":[83],"case":[84],"more":[87],"general":[88],"result,":[89],"\\geq":[98],"n_0$,":[99],"some":[101],"explicitly":[102],"constructed":[103],"number":[104],"$n_0":[105],"\\approx":[106],"1.4":[107],"\\times":[108],"10^{14}$.":[109],"We":[110],"also":[111],"construct":[112],"$\\mathbb{Z}_p$":[117],"primes":[120],"$p":[121,126],"&gt;":[122],"3$":[123],"\\equiv":[127],"3":[128],"\\;":[129],"({\\hbox{mod":[130],"$8$}})$.":[131]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
