{"id":"https://openalex.org/W1817776773","doi":"https://doi.org/10.37236/1789","title":"$q$-Exponential Families","display_name":"$q$-Exponential Families","publication_year":2004,"publication_date":"2004-06-11","ids":{"openalex":"https://openalex.org/W1817776773","doi":"https://doi.org/10.37236/1789","mag":"1817776773"},"language":"en","primary_location":{"id":"doi:10.37236/1789","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1789","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1r36/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/v11i1r36/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":3.7724,"has_fulltext":true,"cited_by_count":31,"citation_normalized_percentile":{"value":0.93054571,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"11","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9997000098228455,"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/T11476","display_name":"Graph theory and applications","score":0.9997000098228455,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9995999932289124,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9993000030517578,"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":0.8235975503921509},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.79584801197052},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.7689520120620728},{"id":"https://openalex.org/keywords/exponential-family","display_name":"Exponential family","score":0.5904704332351685},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.45870932936668396},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4499640166759491},{"id":"https://openalex.org/keywords/exponential-polynomial","display_name":"Exponential polynomial","score":0.4422546625137329},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4409671425819397},{"id":"https://openalex.org/keywords/exponential-sum","display_name":"Exponential sum","score":0.4342602491378784},{"id":"https://openalex.org/keywords/natural-exponential-family","display_name":"Natural exponential family","score":0.43413329124450684},{"id":"https://openalex.org/keywords/deck","display_name":"Deck","score":0.42669111490249634},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.4206886291503906},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4013717770576477},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.38680845499038696},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18144911527633667},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.16221728920936584}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8235975503921509},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.79584801197052},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.7689520120620728},{"id":"https://openalex.org/C55974624","wikidata":"https://www.wikidata.org/wiki/Q1188504","display_name":"Exponential family","level":2,"score":0.5904704332351685},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.45870932936668396},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4499640166759491},{"id":"https://openalex.org/C85384003","wikidata":"https://www.wikidata.org/wiki/Q5421525","display_name":"Exponential polynomial","level":3,"score":0.4422546625137329},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4409671425819397},{"id":"https://openalex.org/C53638454","wikidata":"https://www.wikidata.org/wiki/Q4446020","display_name":"Exponential sum","level":3,"score":0.4342602491378784},{"id":"https://openalex.org/C60775368","wikidata":"https://www.wikidata.org/wiki/Q17099337","display_name":"Natural exponential family","level":3,"score":0.43413329124450684},{"id":"https://openalex.org/C2778966251","wikidata":"https://www.wikidata.org/wiki/Q208123","display_name":"Deck","level":2,"score":0.42669111490249634},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.4206886291503906},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4013717770576477},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38680845499038696},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18144911527633667},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.16221728920936584},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/1789","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1789","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1r36/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:10.1.1.10.6308","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.6308","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_11/PDF/v11i1r36.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.233.9952","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.233.9952","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/0403289v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.3.6235","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.6235","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_11/PostScriptfiles/v11i1r36.ps","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1789","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1789","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1r36/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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1817776773.pdf","grobid_xml":"https://content.openalex.org/works/W1817776773.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W9539176","https://openalex.org/W1594735250","https://openalex.org/W1895916074","https://openalex.org/W1988830734","https://openalex.org/W2072374043","https://openalex.org/W2094801618","https://openalex.org/W2951355421","https://openalex.org/W4253781803","https://openalex.org/W4291474784"],"related_works":["https://openalex.org/W2732416952","https://openalex.org/W4235791879","https://openalex.org/W2619715168","https://openalex.org/W2044705817","https://openalex.org/W2962823242","https://openalex.org/W3034578247","https://openalex.org/W4287761143","https://openalex.org/W2069037953","https://openalex.org/W2083129711","https://openalex.org/W1600199633"],"abstract_inverted_index":{"We":[0],"develop":[1],"an":[2],"analog":[3],"of":[4,8,28,34],"the":[5,12,40,44,48],"exponential":[6,35,41],"families":[7,36],"Wilf":[9],"in":[10],"which":[11],"label":[13],"sets":[14,27],"are":[15,37],"finite":[16,22,26],"dimensional":[17],"vector":[18],"spaces":[19],"over":[20],"a":[21],"field":[23],"rather":[24],"than":[25],"positive":[29],"integers.":[30],"The":[31],"essential":[32],"features":[33],"preserved,":[38],"including":[39],"formula":[42],"relating":[43],"deck":[45],"enumerator":[46],"and":[47],"hand":[49],"enumerator.":[50]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":11}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
