{"id":"https://openalex.org/W2013993584","doi":"https://doi.org/10.1142/s0218196715400135","title":"Factoring Euclidean isometries","display_name":"Factoring Euclidean isometries","publication_year":2015,"publication_date":"2015-01-09","ids":{"openalex":"https://openalex.org/W2013993584","doi":"https://doi.org/10.1142/s0218196715400135","mag":"2013993584"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196715400135","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196715400135","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/A5027495119","display_name":"Noel Brady","orcid":null},"institutions":[{"id":"https://openalex.org/I8692664","display_name":"University of Oklahoma","ror":"https://ror.org/02aqsxs83","country_code":"US","type":"education","lineage":["https://openalex.org/I8692664"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Noel Brady","raw_affiliation_strings":["Department of Mathematics, University of Oklahoma, Norman, OK 73019, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Oklahoma, Norman, OK 73019, USA","institution_ids":["https://openalex.org/I8692664"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048156122","display_name":"Jon McCammond","orcid":null},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jon McCammond","raw_affiliation_strings":["Department of Mathematics, University of California, Santa Barbara, CA 93106, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Santa Barbara, CA 93106, USA","institution_ids":["https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5027495119"],"corresponding_institution_ids":["https://openalex.org/I8692664"],"apc_list":null,"apc_paid":null,"fwci":1.62694579,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.86409785,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"25","issue":"01n02","first_page":"325","last_page":"347"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9980000257492065,"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":0.9980000257492065,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9976000189781189,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9973999857902527,"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/isometry","display_name":"Isometry (Riemannian geometry)","score":0.8896204233169556},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8822092413902283},{"id":"https://openalex.org/keywords/isometry-group","display_name":"Isometry group","score":0.6963841319084167},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5372990965843201},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.519390881061554},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5168552994728088},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.48444652557373047},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.4837625026702881},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4779075086116791},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4387401044368744},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.42879530787467957},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.4117424786090851},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3840411901473999},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10917484760284424}],"concepts":[{"id":"https://openalex.org/C82457910","wikidata":"https://www.wikidata.org/wiki/Q740207","display_name":"Isometry (Riemannian geometry)","level":2,"score":0.8896204233169556},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8822092413902283},{"id":"https://openalex.org/C84160026","wikidata":"https://www.wikidata.org/wiki/Q2211166","display_name":"Isometry group","level":2,"score":0.6963841319084167},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5372990965843201},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.519390881061554},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5168552994728088},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.48444652557373047},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.4837625026702881},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4779075086116791},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4387401044368744},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42879530787467957},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.4117424786090851},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3840411901473999},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10917484760284424},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196715400135","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196715400135","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":[{"id":"https://metadata.un.org/sdg/10","score":0.41999998688697815,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1530075677","https://openalex.org/W1989418639","https://openalex.org/W2019557076","https://openalex.org/W2033117386","https://openalex.org/W2055994721","https://openalex.org/W2064192335","https://openalex.org/W2093397547","https://openalex.org/W2123656616","https://openalex.org/W2134086356","https://openalex.org/W2914659449","https://openalex.org/W2953025710","https://openalex.org/W3102768503","https://openalex.org/W4211184603","https://openalex.org/W4246208316"],"related_works":["https://openalex.org/W2138893893","https://openalex.org/W2352688386","https://openalex.org/W2164954524","https://openalex.org/W1994146144","https://openalex.org/W2154904274","https://openalex.org/W4385849357","https://openalex.org/W2073973324","https://openalex.org/W2053578961","https://openalex.org/W1765759406","https://openalex.org/W1536470053"],"abstract_inverted_index":{"Every":[0],"isometry":[1,26,65],"of":[2,10,16,35,52,63,83,86],"a":[3,8,17,21],"finite-dimensional":[4],"Euclidean":[5],"space":[6,40,85],"is":[7,60,78],"product":[9],"reflections":[11],"and":[12,80],"the":[13,33,64,81,84],"minimum":[14,54],"length":[15,55],"reflection":[18,56],"factorization":[19],"defines":[20],"metric":[22,39],"on":[23,72],"its":[24,53],"full":[25],"group.":[27],"In":[28],"this":[29,38],"paper":[30],"we":[31],"identify":[32],"structure":[34],"intervals":[36],"in":[37,67],"by":[41],"constructing,":[42],"for":[43],"each":[44],"isometry,":[45],"an":[46],"explicit":[47],"combinatorial":[48],"model":[49,59],"encoding":[50],"all":[51],"factorizations.":[57],"The":[58],"largely":[61],"independent":[62],"chosen":[66],"that":[68,88],"it":[69],"only":[70],"depends":[71],"whether":[73],"or":[74],"not":[75],"some":[76],"point":[77],"fixed":[79],"dimension":[82],"directions":[87],"points":[89],"are":[90],"moved.":[91]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
