{"id":"https://openalex.org/W4403096921","doi":"https://doi.org/10.37236/12559","title":"Random Generation of Subgroups of the Modular Group with a Fixed Isomorphism Type","display_name":"Random Generation of Subgroups of the Modular Group with a Fixed Isomorphism Type","publication_year":2024,"publication_date":"2024-10-03","ids":{"openalex":"https://openalex.org/W4403096921","doi":"https://doi.org/10.37236/12559"},"language":"en","primary_location":{"id":"doi:10.37236/12559","is_oa":true,"landing_page_url":"https://doi.org/10.37236/12559","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v31i4p7/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/v31i4p7/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048144277","display_name":"Fr\u00e9d\u00e9rique Bassino","orcid":"https://orcid.org/0000-0002-0127-9352"},"institutions":[{"id":"https://openalex.org/I4210091279","display_name":"Universit\u00e9 Sorbonne Paris Nord","ror":"https://ror.org/0199hds37","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210091279"]},{"id":"https://openalex.org/I51101395","display_name":"Universit\u00e9 Paris 1 Panth\u00e9on-Sorbonne","ror":"https://ror.org/002t25c44","country_code":"FR","type":"education","lineage":["https://openalex.org/I51101395"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Fr\u00e9d\u00e9rique Bassino","raw_affiliation_strings":["Universit\\'e Sorbonne Paris Nord, LIPN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\\'e Sorbonne Paris Nord, LIPN","institution_ids":["https://openalex.org/I4210091279","https://openalex.org/I51101395"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042055476","display_name":"Cyril Nicaud","orcid":"https://orcid.org/0000-0002-8770-0119"},"institutions":[{"id":"https://openalex.org/I4210154111","display_name":"Universit\u00e9 Gustave Eiffel","ror":"https://ror.org/03x42jk29","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210154111"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Cyril Nicaud","raw_affiliation_strings":["LIGM, Univ Gustave Eiffel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIGM, Univ Gustave Eiffel","institution_ids":["https://openalex.org/I4210154111"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5104908604","display_name":"Pascal Weil","orcid":"https://orcid.org/0000-0003-2039-5460"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pascal Weil","raw_affiliation_strings":["CNRS"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.29621381,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"31","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.8592000007629395,"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/T10849","display_name":"Finite Group Theory Research","score":0.8592000007629395,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.8050000071525574,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/conjugacy-class","display_name":"Conjugacy class","score":0.8132740259170532},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7937077879905701},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.7297017574310303},{"id":"https://openalex.org/keywords/psl","display_name":"PSL","score":0.7281565070152283},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6727041006088257},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.6206559538841248},{"id":"https://openalex.org/keywords/modular-group","display_name":"Modular group","score":0.6193743944168091},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.512691855430603},{"id":"https://openalex.org/keywords/finitely-generated-abelian-group","display_name":"Finitely-generated abelian group","score":0.44116297364234924},{"id":"https://openalex.org/keywords/group-isomorphism","display_name":"Group isomorphism","score":0.4262954890727997},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41868066787719727},{"id":"https://openalex.org/keywords/automorphism-group","display_name":"Automorphism group","score":0.1298840343952179},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11530360579490662},{"id":"https://openalex.org/keywords/crystallography","display_name":"Crystallography","score":0.07615014910697937},{"id":"https://openalex.org/keywords/crystal-structure","display_name":"Crystal structure","score":0.052308082580566406}],"concepts":[{"id":"https://openalex.org/C87945829","wikidata":"https://www.wikidata.org/wiki/Q1353233","display_name":"Conjugacy class","level":2,"score":0.8132740259170532},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7937077879905701},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.7297017574310303},{"id":"https://openalex.org/C10464949","wikidata":"https://www.wikidata.org/wiki/Q1914781","display_name":"PSL","level":2,"score":0.7281565070152283},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6727041006088257},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6206559538841248},{"id":"https://openalex.org/C181633103","wikidata":"https://www.wikidata.org/wiki/Q1834342","display_name":"Modular group","level":2,"score":0.6193743944168091},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.512691855430603},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.44116297364234924},{"id":"https://openalex.org/C155190451","wikidata":"https://www.wikidata.org/wiki/Q742064","display_name":"Group isomorphism","level":5,"score":0.4262954890727997},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41868066787719727},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.1298840343952179},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11530360579490662},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.07615014910697937},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.052308082580566406},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C124453015","wikidata":"https://www.wikidata.org/wiki/Q1139583","display_name":"Inner automorphism","level":4,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/12559","is_oa":true,"landing_page_url":"https://doi.org/10.37236/12559","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v31i4p7/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:HAL:hal-04695164v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04695164","pdf_url":"https://hal.science/hal-04695164v1/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"The Electronic Journal of Combinatorics, In press, 31 (4), &#x27E8;10.37236/12559&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.37236/12559","is_oa":true,"landing_page_url":"https://doi.org/10.37236/12559","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v31i4p7/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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4403096921.pdf","grobid_xml":"https://content.openalex.org/works/W4403096921.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2963686177","https://openalex.org/W1506950331","https://openalex.org/W4292743237","https://openalex.org/W2084551772","https://openalex.org/W3022457618","https://openalex.org/W2269408135","https://openalex.org/W2134386818","https://openalex.org/W2147669829","https://openalex.org/W1680814342","https://openalex.org/W3094689178"],"abstract_inverted_index":{"We":[0],"show":[1],"how":[2],"to":[3,26],"efficiently":[4],"count":[5],"and":[6,54],"generate":[7],"uniformly":[8],"at":[9],"random":[10],"finitely":[11,42],"generated":[12,43],"subgroups":[13,67],"of":[14,19,35,45,63,68],"the":[15],"modular":[16],"group":[17],"$\\textsf{PSL}(2,\\mathbb{Z})$":[18,46],"a":[20,32,47,60],"given":[21],"isomorphism":[22],"type.":[23],"The":[24],"method":[25],"achieve":[27],"these":[28],"results":[29],"relies":[30],"on":[31],"natural":[33],"map":[34],"independent":[36],"interest,":[37],"which":[38,49,55],"associates":[39],"with":[40],"any":[41],"subgroup":[44],"graph":[48],"we":[50],"call":[51],"its":[52],"silhouette,":[53],"can":[56],"be":[57],"interpreted":[58],"as":[59],"conjugacy":[61],"class":[62],"free":[64],"finite":[65],"index":[66],"$\\textsf{PSL}(2,\\mathbb{Z})$.":[69]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2024-10-04T00:00:00"}
