{"id":"https://openalex.org/W2133777334","doi":"https://doi.org/10.37236/1959","title":"An Introduction to $q$-Species","display_name":"An Introduction to $q$-Species","publication_year":2005,"publication_date":"2005-11-25","ids":{"openalex":"https://openalex.org/W2133777334","doi":"https://doi.org/10.37236/1959","mag":"2133777334"},"language":"en","primary_location":{"id":"doi:10.37236/1959","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1959","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1r62/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/v12i1r62/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011541907","display_name":"Kent E. Morrison","orcid":"https://orcid.org/0000-0001-5170-4946"},"institutions":[{"id":"https://openalex.org/I149919469","display_name":"California Polytechnic State University","ror":"https://ror.org/001gpfp45","country_code":"US","type":"education","lineage":["https://openalex.org/I149919469"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Kent E. Morrison","raw_affiliation_strings":["Department of Mathematics California Polytechnic State University San Luis Obispo, CA 93407"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics California Polytechnic State University San Luis Obispo, CA 93407","institution_ids":["https://openalex.org/I149919469"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5011541907"],"corresponding_institution_ids":["https://openalex.org/I149919469"],"apc_list":null,"apc_paid":null,"fwci":0.6732,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.73271889,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"12","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.982699990272522,"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":0.982699990272522,"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":0.980400025844574,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9387999773025513,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8604238033294678},{"id":"https://openalex.org/keywords/enumerative-combinatorics","display_name":"Enumerative combinatorics","score":0.8308065533638},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.8018977642059326},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.7101621031761169},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.7091005444526672},{"id":"https://openalex.org/keywords/functor","display_name":"Functor","score":0.6589326858520508},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5033406615257263},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4450902044773102},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39937806129455566},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.38535165786743164},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2873327136039734}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8604238033294678},{"id":"https://openalex.org/C112497148","wikidata":"https://www.wikidata.org/wiki/Q336787","display_name":"Enumerative combinatorics","level":2,"score":0.8308065533638},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.8018977642059326},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.7101621031761169},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.7091005444526672},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.6589326858520508},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5033406615257263},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4450902044773102},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39937806129455566},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38535165786743164},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2873327136039734}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/1959","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1959","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1r62/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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.239.488","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.239.488","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/0512052v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.85.6834","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.85.6834","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_12/PDF/v12i1r62.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1959","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1959","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1r62/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":[{"score":0.4399999976158142,"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2133777334.pdf","grobid_xml":"https://content.openalex.org/works/W2133777334.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1528326162","https://openalex.org/W1574058191","https://openalex.org/W1594735250","https://openalex.org/W1817776773","https://openalex.org/W1976872166","https://openalex.org/W1988830734","https://openalex.org/W2055351834","https://openalex.org/W2094801618","https://openalex.org/W2341751811","https://openalex.org/W4291474784"],"related_works":["https://openalex.org/W4289750385","https://openalex.org/W2883532523","https://openalex.org/W4246811655","https://openalex.org/W2348948427","https://openalex.org/W2042334973","https://openalex.org/W4320035820","https://openalex.org/W2391321755","https://openalex.org/W2127530926","https://openalex.org/W2377983882","https://openalex.org/W2058919198"],"abstract_inverted_index":{"The":[0,61],"combinatorial":[1],"theory":[2,27],"of":[3,14,32,42,48,58,66,77,89],"species":[4],"developed":[5],"by":[6],"Joyal":[7],"provides":[8],"a":[9,67,72,83],"foundation":[10],"for":[11,28],"enumerative":[12,30],"combinatorics":[13,31],"objects":[15,33,44],"constructed":[16,34],"from":[17,35,74],"finite":[18,39,78,84,90],"sets.":[19,91],"In":[20],"this":[21],"paper":[22],"we":[23],"develop":[24],"an":[25],"analogous":[26],"the":[29,75,87],"vector":[36,80],"spaces":[37,81],"over":[38,82],"fields.":[40],"Examples":[41],"these":[43],"include":[45],"subspaces,":[46,49],"flags":[47],"direct":[50],"sum":[51],"decompositions,":[52],"and":[53],"linear":[54],"maps":[55],"or":[56],"matrices":[57],"various":[59],"types.":[60],"unifying":[62],"concept":[63],"is":[64],"that":[65],"\"$q$-species\",":[68],"defined":[69],"to":[70,86],"be":[71],"functor":[73],"category":[76,88],"dimensional":[79],"field":[85]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-15T08:11:43.952461","created_date":"2025-10-10T00:00:00"}