{"id":"https://openalex.org/W2402039133","doi":"https://doi.org/10.1137/17m1148979","title":"Expanding Generating Sets for Solvable Permutation Groups","display_name":"Expanding Generating Sets for Solvable Permutation Groups","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2402039133","doi":"https://doi.org/10.1137/17m1148979","mag":"2402039133"},"language":"en","primary_location":{"id":"doi:10.1137/17m1148979","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1148979","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039975196","display_name":"V. Arvind","orcid":null},"institutions":[{"id":"https://openalex.org/I19149307","display_name":"Chennai Mathematical Institute","ror":"https://ror.org/04zp24820","country_code":"IN","type":"education","lineage":["https://openalex.org/I19149307"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"V. Arvind","raw_affiliation_strings":["Chennai Mathematical Institute"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chennai Mathematical Institute","institution_ids":["https://openalex.org/I19149307"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102818340","display_name":"Partha Mukhopadhyay","orcid":"https://orcid.org/0009-0007-3656-8844"},"institutions":[{"id":"https://openalex.org/I19149307","display_name":"Chennai Mathematical Institute","ror":"https://ror.org/04zp24820","country_code":"IN","type":"education","lineage":["https://openalex.org/I19149307"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Partha Mukhopadhyay","raw_affiliation_strings":["Chennai Mathematical Institute"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chennai Mathematical Institute","institution_ids":["https://openalex.org/I19149307"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042768493","display_name":"Prajakta Nimbhorkar","orcid":"https://orcid.org/0000-0002-7601-9555"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Prajakta Nimbhorkar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5040944160","display_name":"Yadu Vasudev","orcid":"https://orcid.org/0000-0001-7918-7194"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yadu Vasudev","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1263,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.433126,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":"32","issue":"3","first_page":"1721","last_page":"1740"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9991999864578247,"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":0.9991999864578247,"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":0.993399977684021,"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/T11130","display_name":"Coding theory and cryptography","score":0.9927999973297119,"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/combinatorics","display_name":"Combinatorics","score":0.8517733812332153},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7810963988304138},{"id":"https://openalex.org/keywords/permutation-group","display_name":"Permutation group","score":0.6684790253639221},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"Symmetric group","score":0.6641873121261597},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.6631307601928711},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.6063671112060547},{"id":"https://openalex.org/keywords/cayley-graph","display_name":"Cayley graph","score":0.5886631011962891},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.45585641264915466},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4550413489341736},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38428691029548645},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3171952962875366},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08903971314430237}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8517733812332153},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7810963988304138},{"id":"https://openalex.org/C92957085","wikidata":"https://www.wikidata.org/wiki/Q1412905","display_name":"Permutation group","level":3,"score":0.6684790253639221},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.6641873121261597},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.6631307601928711},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.6063671112060547},{"id":"https://openalex.org/C120204988","wikidata":"https://www.wikidata.org/wiki/Q859174","display_name":"Cayley graph","level":3,"score":0.5886631011962891},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.45585641264915466},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4550413489341736},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38428691029548645},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3171952962875366},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08903971314430237},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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":1,"locations":[{"id":"doi:10.1137/17m1148979","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1148979","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322753","display_name":"Infosys Foundation","ror":"https://ror.org/03bs18y54"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1551005442","https://openalex.org/W1982272369","https://openalex.org/W1993524657","https://openalex.org/W2018047324","https://openalex.org/W2049516232","https://openalex.org/W2057648657","https://openalex.org/W2069690626","https://openalex.org/W2086156863","https://openalex.org/W2103998840","https://openalex.org/W2122270497","https://openalex.org/W2158177004","https://openalex.org/W2163137752","https://openalex.org/W4235946010"],"related_works":["https://openalex.org/W2952176788","https://openalex.org/W4291747144","https://openalex.org/W131839596","https://openalex.org/W3133665497","https://openalex.org/W209367526","https://openalex.org/W3013480779","https://openalex.org/W4292719633","https://openalex.org/W2950405155","https://openalex.org/W3013156496","https://openalex.org/W4251766710"],"abstract_inverted_index":{"Let":[0],"$G":[1],"=\\langle":[2],"S\\rangle$":[3],"be":[4],"a":[5,21,31,56,78,85,139,162,170],"solvable":[6,22],"permutation":[7,133],"group":[8,27,134],"given":[9,113,137],"as":[10],"input":[11],"by":[12,114,138],"the":[13,25,49,60,98,166],"generating":[14,39,140,151],"set":[15,40,152],"$S$,":[16],"that":[17,35,48,130,158],"is,":[18],"$G$":[19,46],"is":[20,55,63,161],"subgroup":[23],"of":[24,42,80,89,92,154],"symmetric":[26],"$S_n$.":[28],"We":[29,127],"give":[30],"deterministic":[32,143],"polynomial-time":[33],"algorithm":[34],"computes":[36],"an":[37,149],"expanding":[38,150],"$T$":[41,153],"size":[43,93,107,155],"$\\tilde{O}(n^2(1/\\lambda)^{c})$":[44],"for":[45,97,131],"such":[47,157],"undirected":[50],"Cayley":[51],"graph":[52],"${\\rm":[53,159],"Cay}_u(G,T)$":[54,160],"$\\lambda$-spectral":[57,163],"expander":[58,164],"and":[59,73,101,119],"constant":[61],"$c$":[62],"at":[64],"most":[65],"$8$":[66],"(the":[67],"$\\tilde{O}$":[68],"notation":[69,168],"suppresses":[70],"$\\log":[71,74],"^{O(1)}n$":[72],"^{O(1)}(1/\\lambda)$":[75],"factors).":[76],"As":[77],"byproduct":[79],"our":[81],"proof,":[82],"we":[83,146],"get":[84],"new":[86],"explicit":[87],"construction":[88],"$\\varepsilon$-bias":[90],"spaces":[91],"$\\tilde{O}(n":[94],"(\\log":[95],"d)^{O(1)}(1/\\varepsilon)^{c})$":[96],"groups":[99],"$\\mathbb{Z}_d^n$":[100],"$c\\leq":[102],"8$.":[103],"The":[104],"earlier":[105],"known":[106],"bound":[108],"was":[109],"$O((d":[110],"+":[111],"n/\\varepsilon^2)^{11/2})$":[112],"[Y.":[115],"Azar,":[116],"R.":[117],"Motwani,":[118],"J.":[120],"Naor,":[121],"Combinatorica,":[122],"18":[123],"(1998),":[124],"pp.":[125],"151--171].":[126],"also":[128],"note":[129],"any":[132],"$G\\le":[135],"S_n$":[136],"set,":[141],"in":[142],"polynomial":[144],"time":[145],"can":[147],"compute":[148],"$\\left({n}/{\\lambda}\\right)^{O(1)}$":[156],"where":[165],"$O(1)$":[167],"involves":[169],"large":[171],"constant.":[172]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
