{"id":"https://openalex.org/W3103039525","doi":"https://doi.org/10.1142/s0218196721500363","title":"Linear time algorithm for the conjugacy problem in the first Grigorchuk group","display_name":"Linear time algorithm for the conjugacy problem in the first Grigorchuk group","publication_year":2021,"publication_date":"2021-06-01","ids":{"openalex":"https://openalex.org/W3103039525","doi":"https://doi.org/10.1142/s0218196721500363","mag":"3103039525"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196721500363","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196721500363","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2011.04028","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050287332","display_name":"Mitra Modi","orcid":null},"institutions":[{"id":"https://openalex.org/I108468826","display_name":"Stevens Institute of Technology","ror":"https://ror.org/02z43xh36","country_code":"US","type":"education","lineage":["https://openalex.org/I108468826"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Mitra Modi","raw_affiliation_strings":["Department of Mathematics, Stevens Institute of Technology, Hoboken, NJ, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Stevens Institute of Technology, Hoboken, NJ, USA","institution_ids":["https://openalex.org/I108468826"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059483662","display_name":"Mathew Seedhom","orcid":null},"institutions":[{"id":"https://openalex.org/I108468826","display_name":"Stevens Institute of Technology","ror":"https://ror.org/02z43xh36","country_code":"US","type":"education","lineage":["https://openalex.org/I108468826"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mathew Seedhom","raw_affiliation_strings":["Department of Mathematics, Stevens Institute of Technology, Hoboken, NJ, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Stevens Institute of Technology, Hoboken, NJ, USA","institution_ids":["https://openalex.org/I108468826"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088177875","display_name":"Alexander Ushakov","orcid":"https://orcid.org/0000-0001-9042-7857"},"institutions":[{"id":"https://openalex.org/I108468826","display_name":"Stevens Institute of Technology","ror":"https://ror.org/02z43xh36","country_code":"US","type":"education","lineage":["https://openalex.org/I108468826"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alexander Ushakov","raw_affiliation_strings":["Department of Mathematics, Stevens Institute of Technology, Hoboken, NJ, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Stevens Institute of Technology, Hoboken, NJ, USA","institution_ids":["https://openalex.org/I108468826"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5050287332"],"corresponding_institution_ids":["https://openalex.org/I108468826"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07213477,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"31","issue":"04","first_page":"789","last_page":"806"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9998000264167786,"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/T11567","display_name":"semigroups and automata theory","score":0.9991999864578247,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9987999796867371,"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/conjugacy-class","display_name":"Conjugacy class","score":0.9642853140830994},{"id":"https://openalex.org/keywords/conjugacy-problem","display_name":"Conjugacy problem","score":0.8060479164123535},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.7302070260047913},{"id":"https://openalex.org/keywords/conjugate","display_name":"Conjugate","score":0.7264678478240967},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5966541767120361},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.5678715705871582},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5303234457969666},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5169486403465271},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.44938933849334717},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4133804738521576},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3597814440727234},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13724377751350403},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11629775166511536}],"concepts":[{"id":"https://openalex.org/C87945829","wikidata":"https://www.wikidata.org/wiki/Q1353233","display_name":"Conjugacy class","level":2,"score":0.9642853140830994},{"id":"https://openalex.org/C2780526409","wikidata":"https://www.wikidata.org/wiki/Q5161137","display_name":"Conjugacy problem","level":3,"score":0.8060479164123535},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.7302070260047913},{"id":"https://openalex.org/C197336794","wikidata":"https://www.wikidata.org/wiki/Q5161150","display_name":"Conjugate","level":2,"score":0.7264678478240967},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5966541767120361},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.5678715705871582},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5303234457969666},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5169486403465271},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.44938933849334717},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4133804738521576},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3597814440727234},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13724377751350403},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11629775166511536},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1142/s0218196721500363","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196721500363","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2011.04028","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.04028","pdf_url":"https://arxiv.org/pdf/2011.04028","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3103039525","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2011.04028","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2011.04028","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2011.04028","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2011.04028","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.04028","pdf_url":"https://arxiv.org/pdf/2011.04028","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3103039525.pdf"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1516278578","https://openalex.org/W1526651364","https://openalex.org/W1952479565","https://openalex.org/W1978029823","https://openalex.org/W1984396412","https://openalex.org/W1985108724","https://openalex.org/W1995300673","https://openalex.org/W2002030053","https://openalex.org/W2026853560","https://openalex.org/W2027579516","https://openalex.org/W2033463487","https://openalex.org/W2042740070","https://openalex.org/W2070314356","https://openalex.org/W2138549733","https://openalex.org/W2211936080","https://openalex.org/W2321222144","https://openalex.org/W2334179616","https://openalex.org/W2764050957","https://openalex.org/W2765446779","https://openalex.org/W2962823911","https://openalex.org/W2963909615","https://openalex.org/W3123249926"],"related_works":["https://openalex.org/W3166114698","https://openalex.org/W1986453029","https://openalex.org/W2784995248","https://openalex.org/W2950012869","https://openalex.org/W2913549762","https://openalex.org/W1724861326","https://openalex.org/W2159662747","https://openalex.org/W2135028800","https://openalex.org/W2136231133","https://openalex.org/W2887679466","https://openalex.org/W2144859006","https://openalex.org/W116888106","https://openalex.org/W1979742329","https://openalex.org/W2949476316","https://openalex.org/W2952875504","https://openalex.org/W2736271132","https://openalex.org/W1639028553","https://openalex.org/W2795101523","https://openalex.org/W2519773987","https://openalex.org/W1961817304"],"abstract_inverted_index":{"We":[0,45],"prove":[1],"that":[2,48],"the":[3,7,21],"conjugacy":[4],"problem":[5,22],"in":[6,17,42,63],"first":[8],"Grigorchuk":[9],"group":[10],"[Formula:":[11,30,57],"see":[12,31,58],"text]":[13,32,59],"can":[14,39,60],"be":[15,40,61],"solved":[16,41],"linear":[18,43],"time.":[19,44,65],"Furthermore,":[20],"to":[23],"decide":[24],"if":[25],"a":[26,34,49,52],"list":[27],"of":[28,36,54],"elements":[29,38],"contains":[33],"pair":[35,53],"conjugate":[37,55],"also":[46],"show":[47],"conjugator":[50],"for":[51],"element":[56],"found":[62],"polynomial":[64]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}