{"id":"https://openalex.org/W2999107293","doi":"https://doi.org/10.37236/1044","title":"Lyndon Words and Transition Matrices between Elementary, Homogeneous and Monomial Symmetric Functions","display_name":"Lyndon Words and Transition Matrices between Elementary, Homogeneous and Monomial Symmetric Functions","publication_year":2006,"publication_date":"2006-02-28","ids":{"openalex":"https://openalex.org/W2999107293","doi":"https://doi.org/10.37236/1044","mag":"2999107293"},"language":"en","primary_location":{"id":"doi:10.37236/1044","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1044","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r18/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r18/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011838393","display_name":"Andrius Kulikauskas","orcid":null},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrius Kulikauskas","raw_affiliation_strings":["Minciu Sodas Laboratory Vilnius, Lithuania La Jolla, CA 92093-0112. USA","Department of Mathematics University of California, San Diego La Jolla, CA 92093-0112. USA"],"affiliations":[{"raw_affiliation_string":"Minciu Sodas Laboratory Vilnius, Lithuania La Jolla, CA 92093-0112. USA","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics University of California, San Diego La Jolla, CA 92093-0112. USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113511227","display_name":"Jeffrey B. Remmel","orcid":null},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jeffrey Remmel","raw_affiliation_strings":["Minciu Sodas Laboratory Vilnius, Lithuania La Jolla, CA 92093-0112. USA","Department of Mathematics University of California, San Diego La Jolla, CA 92093-0112. USA"],"affiliations":[{"raw_affiliation_string":"Minciu Sodas Laboratory Vilnius, Lithuania La Jolla, CA 92093-0112. USA","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics University of California, San Diego La Jolla, CA 92093-0112. USA","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5113511227"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.34821053,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"13","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998999834060669,"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/T11567","display_name":"semigroups and automata theory","score":0.9987999796867371,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9973000288009644,"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/monomial","display_name":"Monomial","score":0.9109152555465698},{"id":"https://openalex.org/keywords/symmetric-function","display_name":"Symmetric function","score":0.8732016086578369},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.8201111555099487},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7992425560951233},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.7221572995185852},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6948800086975098},{"id":"https://openalex.org/keywords/elementary-symmetric-polynomial","display_name":"Elementary symmetric polynomial","score":0.5688195824623108},{"id":"https://openalex.org/keywords/partition-function","display_name":"Partition function (quantum field theory)","score":0.5305557250976562},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4726473391056061},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.4481102228164673},{"id":"https://openalex.org/keywords/ring-of-symmetric-functions","display_name":"Ring of symmetric functions","score":0.42486029863357544},{"id":"https://openalex.org/keywords/stanley-symmetric-function","display_name":"Stanley symmetric function","score":0.41167759895324707},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11387690901756287},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.05227804183959961},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.05088302493095398}],"concepts":[{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.9109152555465698},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.8732016086578369},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.8201111555099487},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7992425560951233},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.7221572995185852},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6948800086975098},{"id":"https://openalex.org/C64338288","wikidata":"https://www.wikidata.org/wiki/Q2235316","display_name":"Elementary symmetric polynomial","level":4,"score":0.5688195824623108},{"id":"https://openalex.org/C2778401447","wikidata":"https://www.wikidata.org/wiki/Q7140637","display_name":"Partition function (quantum field theory)","level":2,"score":0.5305557250976562},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4726473391056061},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.4481102228164673},{"id":"https://openalex.org/C156903151","wikidata":"https://www.wikidata.org/wiki/Q17102788","display_name":"Ring of symmetric functions","level":4,"score":0.42486029863357544},{"id":"https://openalex.org/C78136718","wikidata":"https://www.wikidata.org/wiki/Q7600073","display_name":"Stanley symmetric function","level":5,"score":0.41167759895324707},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11387690901756287},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.05227804183959961},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05088302493095398},{"id":"https://openalex.org/C52537462","wikidata":"https://www.wikidata.org/wiki/Q5282055","display_name":"Discrete orthogonal polynomials","level":3,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/1044","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1044","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r18/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/1044","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1044","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r18/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4245115116","display_name":"Combinatorial Structures for Permutation Enumeration and Diagonal Harmonic Modules","funder_award_id":"0400507","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2999107293.pdf","grobid_xml":"https://content.openalex.org/works/W2999107293.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1514324498","https://openalex.org/W1994284482","https://openalex.org/W1999607671","https://openalex.org/W2134984950","https://openalex.org/W2551331446"],"related_works":["https://openalex.org/W2901510162","https://openalex.org/W3045701420","https://openalex.org/W2964348582","https://openalex.org/W2162761802","https://openalex.org/W4211222368","https://openalex.org/W4221162949","https://openalex.org/W1597165749","https://openalex.org/W2062074164","https://openalex.org/W2999107293","https://openalex.org/W1967154553"],"abstract_inverted_index":{"Let":[0],"$h_\\lambda$,":[1],"$e_\\lambda$,":[2],"and":[3,14,43],"$m_\\lambda$":[4,36],"denote":[5],"the":[6,10,15,21,30,44],"homogeneous":[7,40],"symmetric":[8,12,17,41,46],"function,":[9],"elementary":[11,45],"function":[13,18],"monomial":[16],"associated":[19],"with":[20],"partition":[22],"$\\lambda$":[23],"respectively.":[24],"We":[25],"give":[26],"combinatorial":[27],"interpretations":[28],"for":[29],"coefficients":[31,49],"that":[32],"arise":[33],"in":[34,37,52,72],"expanding":[35],"terms":[38,53],"of":[39,54,57,62],"functions":[42],"functions.":[47],"Such":[48],"are":[50],"interpreted":[51],"certain":[55],"classes":[56],"bi-brick":[58],"permutations.":[59],"The":[60],"theory":[61],"Lyndon":[63],"words":[64],"is":[65],"shown":[66],"to":[67],"play":[68],"an":[69],"important":[70],"role":[71],"our":[73],"interpretations.":[74]},"counts_by_year":[{"year":2018,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
