{"id":"https://openalex.org/W4313552038","doi":"https://doi.org/10.1142/s0218196723500157","title":"Degree 2 transformation semigroups as continuous maps on graphs: Complexity and examples","display_name":"Degree 2 transformation semigroups as continuous maps on graphs: Complexity and examples","publication_year":2023,"publication_date":"2023-01-06","ids":{"openalex":"https://openalex.org/W4313552038","doi":"https://doi.org/10.1142/s0218196723500157"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196723500157","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196723500157","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":"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/A5108224750","display_name":"Stuart Margolis","orcid":null},"institutions":[{"id":"https://openalex.org/I13955877","display_name":"Bar-Ilan University","ror":"https://ror.org/03kgsv495","country_code":"IL","type":"education","lineage":["https://openalex.org/I13955877"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Stuart Margolis","raw_affiliation_strings":["Department of Mathematics, Bar Ilan University, 52900 Ramat Gan, Israel"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bar Ilan University, 52900 Ramat Gan, Israel","institution_ids":["https://openalex.org/I13955877"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110160484","display_name":"John Rhodes","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John Rhodes","raw_affiliation_strings":["Department of Mathematics, University of California, Berkeley, California 94720, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Berkeley, California 94720, USA","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5108224750"],"corresponding_institution_ids":["https://openalex.org/I13955877"],"apc_list":null,"apc_paid":null,"fwci":0.2014,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.48632136,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"33","issue":"02","first_page":"289","last_page":"316"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9998999834060669,"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":0.9998999834060669,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9950000047683716,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9850999712944031,"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/mathematics","display_name":"Mathematics","score":0.888304591178894},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.7207772731781006},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.6789018511772156},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.6287157535552979},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5834752321243286},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4821133613586426},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.44937023520469666},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4340447187423706},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17633408308029175},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.056625157594680786}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.888304591178894},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.7207772731781006},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6789018511772156},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.6287157535552979},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5834752321243286},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4821133613586426},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44937023520469666},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4340447187423706},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17633408308029175},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.056625157594680786},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196723500157","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196723500157","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W20560307","https://openalex.org/W36355091","https://openalex.org/W220649288","https://openalex.org/W1518573520","https://openalex.org/W1971297153","https://openalex.org/W1971886993","https://openalex.org/W1979795169","https://openalex.org/W1981565742","https://openalex.org/W1981684679","https://openalex.org/W1989531653","https://openalex.org/W2037840685","https://openalex.org/W2040684427","https://openalex.org/W2046268252","https://openalex.org/W2054978456","https://openalex.org/W2068906344","https://openalex.org/W2157949519","https://openalex.org/W2167954650","https://openalex.org/W2963210887","https://openalex.org/W3137089916","https://openalex.org/W3169383281","https://openalex.org/W4234784553","https://openalex.org/W4293584067"],"related_works":["https://openalex.org/W3161230432","https://openalex.org/W2168900540","https://openalex.org/W4367190712","https://openalex.org/W280458463","https://openalex.org/W1170131723","https://openalex.org/W2399035783","https://openalex.org/W4301429470","https://openalex.org/W2125310826","https://openalex.org/W2369456215","https://openalex.org/W2383559214"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"give":[4,45],"a":[5,37],"number":[6],"of":[7,10,13,35],"illuminating":[8],"examples":[9,46],"transformation":[11,38],"semigroups":[12],"degree":[14],"2":[15],"acting":[16],"on":[17],"graphs":[18],"by":[19,26],"functions":[20],"that":[21,32,47],"preserve":[22],"vertices":[23],"and":[24,59],"edges":[25],"inverse":[27],"image.":[28],"It":[29],"is":[30,40],"known":[31],"the":[33],"complexity":[34,53,57,60],"such":[36],"semigroup":[39],"at":[41],"most":[42],"2.":[43,61],"We":[44],"use":[48],"sophisticated":[49],"lower":[50],"bounds":[51],"to":[52,54],"distinguish":[55],"between":[56],"1":[58]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
