{"id":"https://openalex.org/W1520833852","doi":"https://doi.org/10.37236/1792","title":"Permutations Avoiding Arithmetic Patterns","display_name":"Permutations Avoiding Arithmetic Patterns","publication_year":2004,"publication_date":"2004-06-16","ids":{"openalex":"https://openalex.org/W1520833852","doi":"https://doi.org/10.37236/1792","mag":"1520833852"},"language":"en","primary_location":{"id":"doi:10.37236/1792","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1792","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1r39/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":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":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1r39/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":[],"countries":[],"is_corresponding":true,"raw_author_name":"Peter Hegarty","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5012383867"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.04655273,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"11","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":0.9984999895095825,"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":0.9984999895095825,"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/T12504","display_name":"Mathematics and Applications","score":0.9854999780654907,"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"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9805999994277954,"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/bijection","display_name":"Bijection","score":0.8791406750679016},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8261573910713196},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.8153915405273438},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.7038463354110718},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6911593079566956},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.553691029548645},{"id":"https://openalex.org/keywords/pi","display_name":"Pi","score":0.4270445704460144},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3622433543205261}],"concepts":[{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.8791406750679016},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8261573910713196},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.8153915405273438},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.7038463354110718},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6911593079566956},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.553691029548645},{"id":"https://openalex.org/C53009064","wikidata":"https://www.wikidata.org/wiki/Q167","display_name":"Pi","level":2,"score":0.4270445704460144},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3622433543205261},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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":5,"locations":[{"id":"doi:10.37236/1792","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1792","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1r39/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.6.2620","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.6.2620","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_11/PostScriptfiles/v11i1r39.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.640.1085","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.640.1085","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_11/PDF/v11i1r39.pdf","raw_type":"text"},{"id":"pmh:oai:publications.lib.chalmers.se:60611","is_oa":false,"landing_page_url":"http://publications.lib.chalmers.se/publication/60611-permutations-avoiding-arithmetic-patterns","pdf_url":null,"source":{"id":"https://openalex.org/S4377196909","display_name":"Chalmers Publication Library (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":"Text.Article.Journal.PeerReviewed"},{"id":"pmh:oai:research.chalmers.se:60611","is_oa":false,"landing_page_url":"https://research.chalmers.se/en/publication/60611","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:10.37236/1792","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1792","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1r39/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":null,"license_id":null,"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/W1520833852.pdf","grobid_xml":"https://content.openalex.org/works/W1520833852.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2950642020","https://openalex.org/W1721535522","https://openalex.org/W4386833582","https://openalex.org/W1596411003","https://openalex.org/W4301839635","https://openalex.org/W3004838398","https://openalex.org/W2950417246","https://openalex.org/W4302779826","https://openalex.org/W2258229947","https://openalex.org/W2799131975"],"abstract_inverted_index":{"A":[0],"permutation":[1],"$\\pi$":[2],"of":[3,31,33,58],"an":[4],"abelian":[5,49],"group":[6],"$G$":[7,13],"(that":[8],"is,":[9,47],"a":[10,53,59],"bijection":[11],"from":[12],"to":[14,19],"itself)":[15],"will":[16,62],"be":[17,63],"said":[18],"avoid":[20],"arithmetic":[21],"progressions":[22],"if":[23],"there":[24],"does":[25],"not":[26,35],"exist":[27],"any":[28],"triple":[29],"$(a,b,c)$":[30],"elements":[32],"$G$,":[34],"all":[36],"equal,":[37],"such":[38,52],"that":[39],"$c-b=b-a$":[40],"and":[41,56],"$\\pi(c)-\\pi(b)=\\pi(b)-":[42],"\\pi(a)$.":[43],"The":[44],"basic":[45],"question":[46],"which":[48],"groups":[50],"possess":[51],"permutation?":[54],"This":[55],"problems":[57],"similar":[60],"nature":[61],"considered.":[64]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
