{"id":"https://openalex.org/W1874939446","doi":"https://doi.org/10.37236/2609","title":"Decomposing Sets of Inversions","display_name":"Decomposing Sets of Inversions","publication_year":2013,"publication_date":"2013-02-25","ids":{"openalex":"https://openalex.org/W1874939446","doi":"https://doi.org/10.37236/2609","mag":"1874939446"},"language":"en","primary_location":{"id":"doi:10.37236/2609","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2609","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i1p40/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/v20i1p40/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032425086","display_name":"Lukas Katth\u00e4n","orcid":"https://orcid.org/0000-0002-1456-0514"},"institutions":[{"id":"https://openalex.org/I161103922","display_name":"Philipps University of Marburg","ror":"https://ror.org/01rdrb571","country_code":"DE","type":"education","lineage":["https://openalex.org/I161103922"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Lukas Katth\u00e4n","raw_affiliation_strings":["Philipps-Universit\u00e4t Marburg"],"affiliations":[{"raw_affiliation_string":"Philipps-Universit\u00e4t Marburg","institution_ids":["https://openalex.org/I161103922"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5032425086"],"corresponding_institution_ids":["https://openalex.org/I161103922"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.0478755,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"20","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11567","display_name":"semigroups and automata theory","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9937999844551086,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9896000027656555,"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":0.8497216105461121},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.7685415744781494},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7240279912948608},{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.6909768581390381},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.6537460684776306},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5532146692276001},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.335043340921402}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8497216105461121},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.7685415744781494},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7240279912948608},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.6909768581390381},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.6537460684776306},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5532146692276001},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.335043340921402},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C109007969","wikidata":"https://www.wikidata.org/wiki/Q749565","display_name":"Structural basin","level":2,"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":1,"locations":[{"id":"doi:10.37236/2609","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2609","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i1p40/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"}],"best_oa_location":{"id":"doi:10.37236/2609","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2609","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i1p40/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":[{"id":"https://openalex.org/F4320320875","display_name":"Deutscher Akademischer Austauschdienst","ror":"https://ror.org/039djdh30"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1874939446.pdf","grobid_xml":"https://content.openalex.org/works/W1874939446.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W101814861","https://openalex.org/W112671161","https://openalex.org/W1572527886","https://openalex.org/W1981803420","https://openalex.org/W2000763343","https://openalex.org/W2058773342","https://openalex.org/W2133320102","https://openalex.org/W2153321726","https://openalex.org/W2169540172","https://openalex.org/W2320198223","https://openalex.org/W2962856509","https://openalex.org/W4290379643"],"related_works":["https://openalex.org/W4318195686","https://openalex.org/W2975999359","https://openalex.org/W4287173569","https://openalex.org/W2796561647","https://openalex.org/W4313513739","https://openalex.org/W3119693376","https://openalex.org/W3182422617","https://openalex.org/W2244208494","https://openalex.org/W4280497496","https://openalex.org/W2026358521"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,59],"consider":[4,60],"the":[5,8,38,42,50,61],"question":[6],"how":[7],"set":[9],"of":[10,12,29,41,45,53,64],"inversions":[11],"a":[13],"permutation":[14],"$\\pi":[15],"\\in":[16],"S_n$":[17],"can":[18],"be":[19],"partitioned":[20],"into":[21],"two":[22],"subsets,":[23],"which":[24],"are":[25],"themselves":[26],"inversion":[27,43],"sets":[28],"permutations":[30],"in":[31],"$S_n$.":[32],"Our":[33],"method":[34],"is":[35,55],"to":[36,49],"study":[37],"modular":[39],"decomposition":[40,52],"graph":[44],"$\\pi$.":[46],"A":[47],"correspondence":[48],"substitution":[51],"$\\pi$":[54],"also":[56],"given.":[57],"Moreover,":[58],"special":[62],"case":[63],"multiplicative":[65],"decompositions.":[66]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
