{"id":"https://openalex.org/W2055603882","doi":"https://doi.org/10.1137/s1064827501400278","title":"Card Shuffling and the Polynomial Numerical Hull of Degree <i>k</i>","display_name":"Card Shuffling and the Polynomial Numerical Hull of Degree <i>k</i>","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2055603882","doi":"https://doi.org/10.1137/s1064827501400278","mag":"2055603882"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827501400278","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827501400278","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5019550551","display_name":"Anne Greenbaum","orcid":"https://orcid.org/0000-0002-3783-3466"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Anne Greenbaum","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019550551"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9868,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.77710922,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"25","issue":"2","first_page":"408","last_page":"416"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11716","display_name":"Random Matrices and Applications","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.8803877830505371},{"id":"https://openalex.org/keywords/hull","display_name":"Hull","score":0.6234520673751831},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5819535851478577},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5778969526290894},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5704163908958435},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5611521005630493},{"id":"https://openalex.org/keywords/shuffling","display_name":"Shuffling","score":0.515868067741394},{"id":"https://openalex.org/keywords/numerical-range","display_name":"Numerical range","score":0.49552834033966064},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.47298774123191833},{"id":"https://openalex.org/keywords/polynomial-matrix","display_name":"Polynomial matrix","score":0.4511246085166931},{"id":"https://openalex.org/keywords/homogeneous-polynomial","display_name":"Homogeneous polynomial","score":0.44142773747444153},{"id":"https://openalex.org/keywords/degree-of-a-polynomial","display_name":"Degree of a polynomial","score":0.42736008763313293},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.42141950130462646},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.345161110162735},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2823413014411926}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8803877830505371},{"id":"https://openalex.org/C37423430","wikidata":"https://www.wikidata.org/wiki/Q6750281","display_name":"Hull","level":2,"score":0.6234520673751831},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5819535851478577},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5778969526290894},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5704163908958435},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5611521005630493},{"id":"https://openalex.org/C167927819","wikidata":"https://www.wikidata.org/wiki/Q1930567","display_name":"Shuffling","level":2,"score":0.515868067741394},{"id":"https://openalex.org/C193060811","wikidata":"https://www.wikidata.org/wiki/Q1579053","display_name":"Numerical range","level":2,"score":0.49552834033966064},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.47298774123191833},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.4511246085166931},{"id":"https://openalex.org/C17103678","wikidata":"https://www.wikidata.org/wiki/Q1474074","display_name":"Homogeneous polynomial","level":4,"score":0.44142773747444153},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.42736008763313293},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.42141950130462646},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.345161110162735},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2823413014411926},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C199104240","wikidata":"https://www.wikidata.org/wiki/Q118291","display_name":"Marine engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s1064827501400278","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827501400278","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life below water","id":"https://metadata.un.org/sdg/14","score":0.5600000023841858}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1539593706","https://openalex.org/W2018001888","https://openalex.org/W2024316355","https://openalex.org/W2041214608","https://openalex.org/W2046982553","https://openalex.org/W2080634148","https://openalex.org/W2151609359"],"related_works":["https://openalex.org/W2082590860","https://openalex.org/W2005319551","https://openalex.org/W2009668746","https://openalex.org/W4321367777","https://openalex.org/W2964168342","https://openalex.org/W2035656489","https://openalex.org/W4308266931","https://openalex.org/W2071417418","https://openalex.org/W2964330658","https://openalex.org/W2135696506"],"abstract_inverted_index":{"The":[0],"polynomial":[1,50,118],"numerical":[2,51,119],"hull":[3,52],"of":[4,34,39,45,48,53,85,121],"degree":[5,54],"k":[6,55],"is":[7,20,62,108],"a":[8,16,83,126],"set":[9],"in":[10,65],"the":[11,27,32,37,46,49,58,72,116,130],"complex":[12],"plane":[13],"associated":[14,124],"with":[15,125],"matrix":[17,127],"A":[18,35],"that":[19,61,75],"designed":[21],"to":[22,56,81,110],"give":[23,42],"more":[24],"information":[25],"than":[26],"spectrum":[28],"can":[29],"provide":[30],"about":[31],"behavior":[33],"under":[36],"action":[38],"polynomials.":[40],"We":[41],"an":[43],"example":[44],"application":[47],"explain":[57],"cutoff":[59],"phenomenon":[60],"often":[63],"observed":[64],"Markov":[66],"processes.":[67],"In":[68],"particular,":[69],"we":[70],"consider":[71],"much-publicized":[73],"result":[74,101],"it":[76,107],"takes":[77],"seven":[78],"riffle":[79],"shuffles":[80],"randomize":[82],"deck":[84],"cards":[86],"[D.":[87],"Bayer":[88],"and":[89],"P.":[90],"Diaconis,":[91],"Ann.":[92],"Appl.":[93],"Probab.,":[94],"2":[95],"(1992),":[96],"pp.":[97],"294--313].":[98],"While":[99],"this":[100],"cannot":[102],"be":[103,111],"explained":[104],"by":[105,115],"eigenvalues,":[106],"shown":[109],"very":[112],"well":[113],"predicted":[114],"1-norm":[117],"hulls":[120],"various":[122],"degrees":[123],"derived":[128],"from":[129],"probability":[131],"transition":[132],"matrix.":[133]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
