{"id":"https://openalex.org/W2593602034","doi":"https://doi.org/10.1142/s0218196708004615","title":"NONCOMMUTATIVE SYMMETRIC FUNCTIONS AND THE INVERSION PROBLEM","display_name":"NONCOMMUTATIVE SYMMETRIC FUNCTIONS AND THE INVERSION PROBLEM","publication_year":2008,"publication_date":"2008-08-01","ids":{"openalex":"https://openalex.org/W2593602034","doi":"https://doi.org/10.1142/s0218196708004615","mag":"2593602034"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196708004615","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196708004615","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/A5100744242","display_name":"Wenhua Zhao","orcid":"https://orcid.org/0000-0002-4483-634X"},"institutions":[{"id":"https://openalex.org/I47301684","display_name":"Illinois State University","ror":"https://ror.org/050kcr883","country_code":"US","type":"education","lineage":["https://openalex.org/I47301684"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"WENHUA ZHAO","raw_affiliation_strings":["Department of Mathematics, Illinois State University, Normal, IL 61790-4520, USA","The author has been partially supported by NSA Grant R1-07-0053"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Illinois State University, Normal, IL 61790-4520, USA","institution_ids":["https://openalex.org/I47301684"]},{"raw_affiliation_string":"The author has been partially supported by NSA Grant R1-07-0053","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100744242"],"corresponding_institution_ids":["https://openalex.org/I47301684"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.27930641,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"18","issue":"05","first_page":"869","last_page":"899"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9998999834060669,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9998999834060669,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8151538968086243},{"id":"https://openalex.org/keywords/noncommutative-geometry","display_name":"Noncommutative geometry","score":0.785417914390564},{"id":"https://openalex.org/keywords/formal-power-series","display_name":"Formal power series","score":0.597998857498169},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.4888250231742859},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.47602608799934387},{"id":"https://openalex.org/keywords/homomorphism","display_name":"Homomorphism","score":0.4671606123447418},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.45852580666542053},{"id":"https://openalex.org/keywords/hopf-algebra","display_name":"Hopf algebra","score":0.4556659758090973},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.39727964997291565},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35795342922210693},{"id":"https://openalex.org/keywords/power-series","display_name":"Power series","score":0.32660841941833496},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3257324695587158},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08676883578300476}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8151538968086243},{"id":"https://openalex.org/C68797384","wikidata":"https://www.wikidata.org/wiki/Q2746792","display_name":"Noncommutative geometry","level":2,"score":0.785417914390564},{"id":"https://openalex.org/C151746172","wikidata":"https://www.wikidata.org/wiki/Q1003025","display_name":"Formal power series","level":3,"score":0.597998857498169},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.4888250231742859},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.47602608799934387},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.4671606123447418},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.45852580666542053},{"id":"https://openalex.org/C29712632","wikidata":"https://www.wikidata.org/wiki/Q1627597","display_name":"Hopf algebra","level":3,"score":0.4556659758090973},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39727964997291565},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35795342922210693},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.32660841941833496},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3257324695587158},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08676883578300476}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218196708004615","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196708004615","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:CiteSeerX.psu:10.1.1.237.5020","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.237.5020","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0509135v2.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W131742520","https://openalex.org/W163421878","https://openalex.org/W173417592","https://openalex.org/W571001201","https://openalex.org/W582871954","https://openalex.org/W1493656640","https://openalex.org/W1583189483","https://openalex.org/W1659648688","https://openalex.org/W1797987301","https://openalex.org/W1971356298","https://openalex.org/W1996204119","https://openalex.org/W1999997928","https://openalex.org/W2004548010","https://openalex.org/W2015310823","https://openalex.org/W2015501897","https://openalex.org/W2035280681","https://openalex.org/W2039727649","https://openalex.org/W2041430670","https://openalex.org/W2043056264","https://openalex.org/W2044413922","https://openalex.org/W2050410364","https://openalex.org/W2052385785","https://openalex.org/W2068842685","https://openalex.org/W2081461845","https://openalex.org/W2113547185","https://openalex.org/W2134984950","https://openalex.org/W2158031396","https://openalex.org/W4234417351","https://openalex.org/W4253289064"],"related_works":["https://openalex.org/W467679","https://openalex.org/W3117105351","https://openalex.org/W1999045233","https://openalex.org/W131037327","https://openalex.org/W2044685772","https://openalex.org/W2504047832","https://openalex.org/W3181346485","https://openalex.org/W1964720703","https://openalex.org/W3028536017","https://openalex.org/W2066453456"],"abstract_inverted_index":{"Let":[0,24],"K":[1],"be":[2,26],"any":[3,117],"unital":[4],"commutative":[5,20],"\u211a-algebra":[6],"and":[7,31,64,141,176,182,189],"z":[8,13,17,39,51],"=":[9,50,62],"(z":[10],"1":[11],",":[12,15],"2":[14],"\u2026,":[16],"n":[18],")":[19,175],"or":[21],"noncommutative":[22],"variables.":[23],"t":[25,48,54,78,131,166,174,188,198],"a":[27,68,85,111,203],"formal":[28,34,184],"central":[29],"parameter":[30],"K[[t]]\u3008\u3008z\u3009\u3009":[32,57],"the":[33,93,114,124,142,162,168,180,183,193,206],"power":[35],"series":[36,170],"algebra":[37,87,95],"of":[38,56,100,120,136,158,172,186,196,205],"over":[40],"K[[t]].":[41],"In":[42,105],"[29],":[43],"for":[44,113,167,192],"each":[45],"automorphism":[46],"F":[47,77,130,165,187,197],"(z)":[49,55,61],"-":[52],"H":[53,59],"with":[58,210],"t=0":[60],"0":[63],"o(H(z))":[65],"\u2265":[66],"1,":[67],"[Formula:":[69,89,96,125,144,177],"see":[70,90,97,126,145,178],"text]":[71,91,98,127],"(noncommutative":[72,102],"symmetric)":[73],"system":[74,128,163],"[28]":[75],"\u03a9":[76,129,164],"has":[79],"been":[80],"constructed.":[81],"Consequently,":[82],"we":[83,108,148,201],"get":[84],"Hopf":[86,94],"homomorphism":[88,143],"from":[92],"[9]":[99,140],"NCSFs":[101,137],"symmetric":[103],"functions).":[104],"this":[106],"paper,":[107],"first":[109],"give":[110],"list":[112],"identities":[115,135,151],"between":[116],"two":[118],"sequences":[119],"differential":[121,159],"operators":[122],"in":[123,139,156,161],"by":[132],"using":[133],"some":[134,154],"derived":[138],"text].":[146],"Secondly,":[147],"apply":[149],"these":[150],"to":[152],"derive":[153],"formulas":[155,191],"terms":[157],"operator":[160],"Taylor":[169],"expansions":[171],"u(F":[173],"text];":[179],"D-Log":[181],"flow":[185],"inversion":[190],"inverse":[194],"map":[195],".":[199],"Finally,":[200],"discuss":[202],"connection":[204],"well-known":[207],"Jacobian":[208],"conjecture":[209],"NCSFs.":[211]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
