{"id":"https://openalex.org/W2069894557","doi":"https://doi.org/10.1155/2012/424189","title":"Symmetry Fermionic -Adic -Integral on for Eulerian Polynomials","display_name":"Symmetry Fermionic -Adic -Integral on for Eulerian Polynomials","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2069894557","doi":"https://doi.org/10.1155/2012/424189","mag":"2069894557"},"language":"en","primary_location":{"id":"doi:10.1155/2012/424189","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2012/424189","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/424189.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2012/424189.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028620250","display_name":"Daeyeoul Kim","orcid":"https://orcid.org/0000-0002-2970-1666"},"institutions":[{"id":"https://openalex.org/I4210158432","display_name":"National Institute for Mathematical Sciences","ror":"https://ror.org/04n7py080","country_code":"KR","type":"education","lineage":["https://openalex.org/I4210158432"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Daeyeoul Kim","raw_affiliation_strings":["National Institute for Mathematical Sciences, Yuseong-daero 1689-gil, Yuseong-gu, Daejeon 305-811, Republic of Korea"],"affiliations":[{"raw_affiliation_string":"National Institute for Mathematical Sciences, Yuseong-daero 1689-gil, Yuseong-gu, Daejeon 305-811, Republic of Korea","institution_ids":["https://openalex.org/I4210158432"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100362658","display_name":"Min-Soo Kim","orcid":"https://orcid.org/0000-0002-1867-0817"},"institutions":[{"id":"https://openalex.org/I71007489","display_name":"Kyungnam University","ror":"https://ror.org/037pkxm09","country_code":"KR","type":"education","lineage":["https://openalex.org/I71007489"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Min-Soo Kim","raw_affiliation_strings":["Division of Cultural Education, Kyungnam University, Changwon 631-701, Republic of Korea"],"affiliations":[{"raw_affiliation_string":"Division of Cultural Education, Kyungnam University, Changwon 631-701, Republic of Korea","institution_ids":["https://openalex.org/I71007489"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100362658"],"corresponding_institution_ids":["https://openalex.org/I71007489"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.16205889,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"2012","issue":null,"first_page":"1","last_page":"7"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9998999834060669,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9943000078201294,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9909999966621399,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8969007730484009},{"id":"https://openalex.org/keywords/eulerian-path","display_name":"Eulerian path","score":0.8797265887260437},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.6164743304252625},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.5919263958930969},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.5107123851776123},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.48784303665161133},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4850877821445465},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4812147915363312},{"id":"https://openalex.org/keywords/power-sum-symmetric-polynomial","display_name":"Power sum symmetric polynomial","score":0.4665868878364563},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4227645695209503},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38145017623901367},{"id":"https://openalex.org/keywords/discrete-orthogonal-polynomials","display_name":"Discrete orthogonal polynomials","score":0.3789226710796356},{"id":"https://openalex.org/keywords/wilson-polynomials","display_name":"Wilson polynomials","score":0.37340492010116577},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.34224000573158264},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.340939998626709},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3180965483188629},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09812533855438232}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8969007730484009},{"id":"https://openalex.org/C43058520","wikidata":"https://www.wikidata.org/wiki/Q624580","display_name":"Eulerian path","level":3,"score":0.8797265887260437},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.6164743304252625},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5919263958930969},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.5107123851776123},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.48784303665161133},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4850877821445465},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4812147915363312},{"id":"https://openalex.org/C129010115","wikidata":"https://www.wikidata.org/wiki/Q1298683","display_name":"Power sum symmetric polynomial","level":5,"score":0.4665868878364563},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4227645695209503},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38145017623901367},{"id":"https://openalex.org/C52537462","wikidata":"https://www.wikidata.org/wiki/Q5282055","display_name":"Discrete orthogonal polynomials","level":3,"score":0.3789226710796356},{"id":"https://openalex.org/C43176163","wikidata":"https://www.wikidata.org/wiki/Q8023263","display_name":"Wilson polynomials","level":4,"score":0.37340492010116577},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.34224000573158264},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.340939998626709},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3180965483188629},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09812533855438232},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2012/424189","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2012/424189","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/424189.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:752f50915987429a8bcba504af10e9dd","is_oa":true,"landing_page_url":"https://doaj.org/article/752f50915987429a8bcba504af10e9dd","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2012 (2012)","raw_type":"article"},{"id":"pmh:oai:hindawi.com:10.1155/2012/424189","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/424189","pdf_url":null,"source":{"id":"https://openalex.org/S4306400340","display_name":"Hindawi Journal of Chemistry (Hindawi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210126990","host_organization_name":"Hindawi (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210126990"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Research Article"}],"best_oa_location":{"id":"doi:10.1155/2012/424189","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2012/424189","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/424189.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321271","display_name":"Kyungnam University","ror":"https://ror.org/037pkxm09"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2069894557.pdf","grobid_xml":"https://content.openalex.org/works/W2069894557.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W1983951523","https://openalex.org/W1998563024","https://openalex.org/W2021097183","https://openalex.org/W2025354028","https://openalex.org/W2071565129","https://openalex.org/W2194946137"],"related_works":["https://openalex.org/W2070537393","https://openalex.org/W3125460591","https://openalex.org/W2788208119","https://openalex.org/W3147630167","https://openalex.org/W2168893271","https://openalex.org/W34992575","https://openalex.org/W2132314122","https://openalex.org/W4286909400","https://openalex.org/W2035948520","https://openalex.org/W4313408517"],"abstract_inverted_index":{"Kim":[0,49],"et":[1],"al.":[2],"(2012)":[3],"introduced":[4],"an":[5],"interesting":[6],"p":[7,41],"-adic":[8,42],"analogue":[9],"of":[10,38,60,64],"the":[11,19,25,36,39,57,61,68],"Eulerian":[12,20,69],"polynomials.":[13,70],"They":[14],"studied":[15],"some":[16],"identities":[17],"on":[18,45],"polynomials":[21],"in":[22],"connection":[23],"with":[24],"Genocchi,":[26],"Euler,":[27],"and":[28,67],"tangent":[29],"numbers.":[30],"In":[31],"this":[32],"paper,":[33],"by":[34,48],"applying":[35],"symmetry":[37],"fermionic":[40],"q":[43,58],"-integral":[44],",":[46],"defined":[47],"(2008),":[50],"we":[51],"show":[52],"a":[53],"symmetric":[54],"relation":[55],"between":[56],"-extension":[59],"alternating":[62],"sum":[63],"integer":[65],"powers":[66]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}