{"id":"https://openalex.org/W2962733587","doi":"https://doi.org/10.37236/5264","title":"Overview on Heisenberg—Weyl Algebra and Subsets of Riordan Subgroups","display_name":"Overview on Heisenberg—Weyl Algebra and Subsets of Riordan Subgroups","publication_year":2015,"publication_date":"2015-10-30","ids":{"openalex":"https://openalex.org/W2962733587","doi":"https://doi.org/10.37236/5264","mag":"2962733587"},"language":"en","primary_location":{"id":"doi:10.37236/5264","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5264","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i4p16/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/v22i4p16/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088224557","display_name":"Silvia Goodenough","orcid":null},"institutions":[{"id":"https://openalex.org/I4210091279","display_name":"Universit\u00e9 Sorbonne Paris Nord","ror":"https://ror.org/0199hds37","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210091279"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I4210091437","display_name":"Sorbonne Paris Cit\u00e9","ror":"https://ror.org/001z21q04","country_code":"FR","type":"other","lineage":["https://openalex.org/I4210091437"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Silvia Goodenough","raw_affiliation_strings":["Institut Galil\u00e9e\r\nUniversit\u00e9 Paris 13, Sorbonne Paris Cit\u00e9","Institut Galil\u00e9e\nUniversit\u00e9 Paris 13, Sorbonne Paris Cit\u00e9"],"affiliations":[{"raw_affiliation_string":"Institut Galil\u00e9e\r\nUniversit\u00e9 Paris 13, Sorbonne Paris Cit\u00e9","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I4210091437","https://openalex.org/I4210091279"]},{"raw_affiliation_string":"Institut Galil\u00e9e\nUniversit\u00e9 Paris 13, Sorbonne Paris Cit\u00e9","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I4210091437","https://openalex.org/I4210091279"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027581014","display_name":"Christian Lavault","orcid":null},"institutions":[{"id":"https://openalex.org/I4210091437","display_name":"Sorbonne Paris Cit\u00e9","ror":"https://ror.org/001z21q04","country_code":"FR","type":"other","lineage":["https://openalex.org/I4210091437"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I4210091279","display_name":"Universit\u00e9 Sorbonne Paris Nord","ror":"https://ror.org/0199hds37","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210091279"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Christian Lavault","raw_affiliation_strings":["Institut Galil\u00e9e\r\nUniversit\u00e9 Paris 13, Sorbonne Paris Cit\u00e9","Institut Galil\u00e9e\nUniversit\u00e9 Paris 13, Sorbonne Paris Cit\u00e9"],"affiliations":[{"raw_affiliation_string":"Institut Galil\u00e9e\r\nUniversit\u00e9 Paris 13, Sorbonne Paris Cit\u00e9","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I4210091437","https://openalex.org/I4210091279"]},{"raw_affiliation_string":"Institut Galil\u00e9e\nUniversit\u00e9 Paris 13, Sorbonne Paris Cit\u00e9","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I4210091437","https://openalex.org/I4210091279"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5088224557"],"corresponding_institution_ids":["https://openalex.org/I204730241","https://openalex.org/I4210091279","https://openalex.org/I4210091437"],"apc_list":null,"apc_paid":null,"fwci":1.344,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.80789336,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"22","issue":"4","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/T11428","display_name":"Advanced Mathematical Identities","score":0.9850000143051147,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9693999886512756,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7298570275306702},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5744691491127014},{"id":"https://openalex.org/keywords/heisenberg-group","display_name":"Heisenberg group","score":0.5450218319892883},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5389488339424133},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5273246169090271},{"id":"https://openalex.org/keywords/weyl-group","display_name":"Weyl group","score":0.5095022320747375},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.48185762763023376},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.45827579498291016},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.12408936023712158},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11380618810653687},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06635165214538574}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7298570275306702},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5744691491127014},{"id":"https://openalex.org/C127519595","wikidata":"https://www.wikidata.org/wiki/Q1601337","display_name":"Heisenberg group","level":2,"score":0.5450218319892883},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5389488339424133},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5273246169090271},{"id":"https://openalex.org/C40233952","wikidata":"https://www.wikidata.org/wiki/Q768074","display_name":"Weyl group","level":2,"score":0.5095022320747375},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.48185762763023376},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.45827579498291016},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.12408936023712158},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11380618810653687},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06635165214538574}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/5264","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5264","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i4p16/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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:10.37236/5264","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5264","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i4p16/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2962733587.pdf","grobid_xml":"https://content.openalex.org/works/W2962733587.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W18020221","https://openalex.org/W186403072","https://openalex.org/W634966607","https://openalex.org/W656285810","https://openalex.org/W972589330","https://openalex.org/W1489988510","https://openalex.org/W1563213005","https://openalex.org/W1594563152","https://openalex.org/W1677718101","https://openalex.org/W1992020206","https://openalex.org/W1994702412","https://openalex.org/W2021692008","https://openalex.org/W2022583102","https://openalex.org/W2023120017","https://openalex.org/W2035311210","https://openalex.org/W2039343706","https://openalex.org/W2039370477","https://openalex.org/W2044408173","https://openalex.org/W2048936241","https://openalex.org/W2050635669","https://openalex.org/W2074388774","https://openalex.org/W2080115203","https://openalex.org/W2081783255","https://openalex.org/W2083981160","https://openalex.org/W2125089797","https://openalex.org/W2126209209","https://openalex.org/W2144923576","https://openalex.org/W2160448281","https://openalex.org/W2318592054","https://openalex.org/W2332058888","https://openalex.org/W2408733897","https://openalex.org/W3032991774","https://openalex.org/W3106094500","https://openalex.org/W4210629339","https://openalex.org/W4230118372","https://openalex.org/W4234748143","https://openalex.org/W4285719527","https://openalex.org/W4300302225","https://openalex.org/W6600339457","https://openalex.org/W6600892083","https://openalex.org/W6604202342","https://openalex.org/W6607049896","https://openalex.org/W6631387319"],"related_works":["https://openalex.org/W1981036054","https://openalex.org/W187158282","https://openalex.org/W2963135356","https://openalex.org/W4297817068","https://openalex.org/W1983151614","https://openalex.org/W99100235","https://openalex.org/W2081214999","https://openalex.org/W4385288644","https://openalex.org/W2046144884","https://openalex.org/W2015805882"],"abstract_inverted_index":{"In":[0],"a":[1,78,82],"first":[2],"part,":[3],"we":[4],"are":[5,59,84,93],"concerned":[6],"with":[7,24,54],"the":[8,13,17,28,34,40,47,66,73,98],"relationships":[9],"between":[10],"polynomials":[11],"in":[12,62,65,72,97],"two":[14],"generators":[15],"of":[16,19,42,50],"algebra":[18],"Heisenberg\u2014Weyl,":[20],"its":[21],"Bargmann\u2014Fock":[22],"representation":[23],"differential":[25],"operators":[26],"and":[27,81],"associated":[29,45],"one-parameter":[30],"group.Upon":[31],"this":[32],"basis,":[33],"paper":[35],"is":[36],"then":[37],"devoted":[38],"to":[39,46,90],"groups":[41],"Riordan":[43,63,67,75],"matrices":[44,51],"related":[48],"transformations":[49],"(i.e.,":[52],"substitutions":[53],"prefunctions).":[55],"Thereby,":[56],"various":[57],"properties":[58],"studied":[60],"arising":[61],"arrays,":[64],"group":[68],"and,":[69],"more":[70],"specifically,":[71],"\"striped\"":[74],"subgroups;":[76],"further,":[77],"striped":[79],"quasigroup":[80],"semigroup":[83],"also":[85,94],"examined.":[86],"A":[87],"few":[88],"applications":[89],"combinatorial":[91],"structures":[92],"briefly":[95],"addressed":[96],"Appendix.":[99]},"counts_by_year":[{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}