{"id":"https://openalex.org/W3000608781","doi":"https://doi.org/10.37236/8678","title":"Permutations with orders coprime to a given integer","display_name":"Permutations with orders coprime to a given integer","publication_year":2020,"publication_date":"2020-01-10","ids":{"openalex":"https://openalex.org/W3000608781","doi":"https://doi.org/10.37236/8678","mag":"3000608781"},"language":"en","primary_location":{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/5c248b84-022c-4a3e-82e9-7ab943d69a59","is_oa":true,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/5c248b84-022c-4a3e-82e9-7ab943d69a59","pdf_url":"https://research-information.bris.ac.uk/files/220773477/Full_text_PDF_final_published_version_.pdf","source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nd","license_id":"https://openalex.org/licenses/cc-by-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Harper, S, Praeger, C, Glasby, S & Bamberg, J 2020, 'Permutations with orders coprime to a given integer', Electronic Journal of Combinatorics, vol. 27, no. 1, P1.6. https://doi.org/10.37236/8678","raw_type":"info:eu-repo/semantics/publishedVersion"},"type":"article","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research-information.bris.ac.uk/files/220773477/Full_text_PDF_final_published_version_.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087244891","display_name":"Scott Harper","orcid":"https://orcid.org/0000-0002-0056-2914"},"institutions":[{"id":"https://openalex.org/I177877127","display_name":"The University of Western Australia","ror":"https://ror.org/047272k79","country_code":"AU","type":"education","lineage":["https://openalex.org/I177877127"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Scott Harper","raw_affiliation_strings":["School of Mathematics","The University of Western Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics","institution_ids":[]},{"raw_affiliation_string":"The University of Western Australia","institution_ids":["https://openalex.org/I177877127"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043525348","display_name":"Cheryl E. Praeger","orcid":"https://orcid.org/0000-0002-0881-7336"},"institutions":[{"id":"https://openalex.org/I177877127","display_name":"The University of Western Australia","ror":"https://ror.org/047272k79","country_code":"AU","type":"education","lineage":["https://openalex.org/I177877127"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Cheryl Praeger","raw_affiliation_strings":["University of Western Australia","Centre for the Mathematics of Symmetry and Computation, Department of Mathematics and Statistics, University of Western Australia, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Western Australia","institution_ids":["https://openalex.org/I177877127"]},{"raw_affiliation_string":"Centre for the Mathematics of Symmetry and Computation, Department of Mathematics and Statistics, University of Western Australia, Australia","institution_ids":["https://openalex.org/I177877127"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Stephen Glasby","orcid":null},"institutions":[{"id":"https://openalex.org/I177877127","display_name":"The University of Western Australia","ror":"https://ror.org/047272k79","country_code":"AU","type":"education","lineage":["https://openalex.org/I177877127"]},{"id":"https://openalex.org/I178535277","display_name":"University of the West of England","ror":"https://ror.org/02nwg5t34","country_code":"GB","type":"education","lineage":["https://openalex.org/I178535277"]},{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["AU","GB"],"is_corresponding":false,"raw_author_name":"Stephen Glasby","raw_affiliation_strings":["University of Western Australia","School of Mathematics, The University of Bristol, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Western Australia","institution_ids":["https://openalex.org/I177877127"]},{"raw_affiliation_string":"School of Mathematics, The University of Bristol, United Kingdom","institution_ids":["https://openalex.org/I36234482","https://openalex.org/I178535277"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038799614","display_name":"John Bamberg","orcid":"https://orcid.org/0000-0001-7347-8687"},"institutions":[{"id":"https://openalex.org/I177877127","display_name":"The University of Western Australia","ror":"https://ror.org/047272k79","country_code":"AU","type":"education","lineage":["https://openalex.org/I177877127"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"John Bamberg","raw_affiliation_strings":["University of Western Australia","Centre for the Mathematics of Symmetry and Computation, Department of Mathematics and Statistics, University of Western Australia, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Western Australia","institution_ids":["https://openalex.org/I177877127"]},{"raw_affiliation_string":"Centre for the Mathematics of Symmetry and Computation, Department of Mathematics and Statistics, University of Western Australia, Australia","institution_ids":["https://openalex.org/I177877127"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.2854,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.91571824,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9929999709129333,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9929999709129333,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9904999732971191,"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"}},{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9829999804496765,"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/combinatorics","display_name":"Combinatorics","score":0.8780721426010132},{"id":"https://openalex.org/keywords/coprime-integers","display_name":"Coprime integers","score":0.860906720161438},{"id":"https://openalex.org/keywords/eulers-totient-function","display_name":"Euler's totient function","score":0.7868086099624634},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7424100637435913},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.7275618314743042},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.7097235918045044},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.45048758387565613},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.425989031791687},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.36539435386657715},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12543487548828125}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8780721426010132},{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.860906720161438},{"id":"https://openalex.org/C198944804","wikidata":"https://www.wikidata.org/wiki/Q190026","display_name":"Euler's totient function","level":3,"score":0.7868086099624634},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7424100637435913},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.7275618314743042},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.7097235918045044},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.45048758387565613},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.425989031791687},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.36539435386657715},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12543487548828125},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","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},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/5c248b84-022c-4a3e-82e9-7ab943d69a59","is_oa":true,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/5c248b84-022c-4a3e-82e9-7ab943d69a59","pdf_url":"https://research-information.bris.ac.uk/files/220773477/Full_text_PDF_final_published_version_.pdf","source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nd","license_id":"https://openalex.org/licenses/cc-by-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Harper, S, Praeger, C, Glasby, S & Bamberg, J 2020, 'Permutations with orders coprime to a given integer', Electronic Journal of Combinatorics, vol. 27, no. 1, P1.6. https://doi.org/10.37236/8678","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/5c248b84-022c-4a3e-82e9-7ab943d69a59","is_oa":true,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/5c248b84-022c-4a3e-82e9-7ab943d69a59","pdf_url":"https://research-information.bris.ac.uk/files/220773477/Full_text_PDF_final_published_version_.pdf","source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nd","license_id":"https://openalex.org/licenses/cc-by-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Harper, S, Praeger, C, Glasby, S & Bamberg, J 2020, 'Permutations with orders coprime to a given integer', Electronic Journal of Combinatorics, vol. 27, no. 1, P1.6. https://doi.org/10.37236/8678","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3000608781.pdf","grobid_xml":"https://content.openalex.org/works/W3000608781.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1972915471","https://openalex.org/W1974157424","https://openalex.org/W1976677460","https://openalex.org/W1988782547","https://openalex.org/W1999012586","https://openalex.org/W2027920677","https://openalex.org/W2094085034","https://openalex.org/W2110522712","https://openalex.org/W2128861872","https://openalex.org/W2134606481","https://openalex.org/W2227548006","https://openalex.org/W2369713881","https://openalex.org/W4230925302","https://openalex.org/W4239913611"],"related_works":["https://openalex.org/W4287724211","https://openalex.org/W3183648988","https://openalex.org/W3041044038","https://openalex.org/W2053870354","https://openalex.org/W4309796663","https://openalex.org/W3164481304","https://openalex.org/W4315651153","https://openalex.org/W2243579381","https://openalex.org/W4250406566","https://openalex.org/W2901498436"],"abstract_inverted_index":{"Let":[0],"m":[1,33,34,36],"be":[2,10],"a":[3,38,48],"positive":[4,49],"integer":[5],"and":[6],"let":[7],"(m,":[8],"n)":[9],"the":[11,16],"proportion":[12],"of":[13,15,42],"permutations":[14],"symmetric":[17],"group":[18],"Sym(n)":[19],"whose":[20],"order":[21],"is":[22,37,58],"coprime":[23],"to":[24],"m.In":[25],"2002,":[26],"Pouyanne":[27],"proved":[28],"that":[29,45],"(n,":[30],"m)n":[31],"1-(m)":[32],"where":[35],"complicated":[39],"(unbounded)":[40],"function":[41],"m.We":[43],"show":[44],"there":[46],"exists":[47],"constant":[50],"C(m)":[51],"such":[52],"that,":[53],"for":[54],"all":[55],"n":[56],"m,where":[57],"Euler's":[59],"totient":[60],"function.":[61]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}