{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:33:38Z","timestamp":1760240018080,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,2,22]],"date-time":"2019-02-22T00:00:00Z","timestamp":1550793600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we introduce central complete and incomplete Bell polynomials which can be viewed as generalizations of central Bell polynomials and central factorial numbers of the second kind, and also as \u2019central\u2019 analogues for complete and incomplete Bell polynomials. Further, some properties and identities for these polynomials are investigated. In particular, we provide explicit formulas for the central complete and incomplete Bell polynomials related to central factorial numbers of the second kind.<\/jats:p>","DOI":"10.3390\/sym11020288","type":"journal-article","created":{"date-parts":[[2019,2,22]],"date-time":"2019-02-22T11:26:14Z","timestamp":1550834774000},"page":"288","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["On Central Complete and Incomplete Bell Polynomials I"],"prefix":"10.3390","volume":"11","author":[{"given":"Taekyun","family":"Kim","sequence":"first","affiliation":[{"name":"Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9599-7015","authenticated-orcid":false,"given":"Dae San","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sogang University, Seoul 121-742, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gwan-Woo","family":"Jang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"013510","DOI":"10.1063\/1.3530867","article-title":"Representable states on quasilocal quasi*-algebras","volume":"52","author":"Bagarello","year":"2011","journal-title":"J. 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