{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T15:57:40Z","timestamp":1765382260479,"version":"build-2065373602"},"reference-count":93,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,8,31]],"date-time":"2020-08-31T00:00:00Z","timestamp":1598832000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Education (Republic of Korea)","award":["NRF-2020R111A1A01052440"],"award-info":[{"award-number":["NRF-2020R111A1A01052440"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The q-Stirling numbers (polynomials) of the second kind have been investigated and applied in a variety of research subjects including, even, the q-analogue of Bernstein polynomials. The (p,q)-Stirling numbers (polynomials) of the second kind have been studied, particularly, in relation to combinatorics. In this paper, we aim to introduce new (p,q)-Stirling polynomials of the second kind which are shown to be fit for the (p,q)-analogue of Bernstein polynomials. We also present some interesting identities involving the (p,q)-binomial coefficients. We further discuss certain vanishing identities associated with the q-and (p,q)-Stirling polynomials of the second kind.<\/jats:p>","DOI":"10.3390\/sym12091436","type":"journal-article","created":{"date-parts":[[2020,8,31]],"date-time":"2020-08-31T21:41:23Z","timestamp":1598910083000},"page":"1436","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Certain Identities Associated with (p,q)-Binomial Coefficients and (p,q)-Stirling Polynomials of the Second Kind"],"prefix":"10.3390","volume":"12","author":[{"given":"Talha","family":"Usman","sequence":"first","affiliation":[{"name":"Department of Mathematics, School of Basic and Applied Sciences, Lingaya\u2019s Vidyapeeth, Faridabad-121002, Haryana, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2719-6002","authenticated-orcid":false,"given":"Mohd","family":"Saif","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Aligarh Muslim University, Aligarh- 202002, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junesang","family":"Choi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Dongguk University, Gyeongju 38066, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,8,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"987","DOI":"10.1215\/S0012-7094-48-01588-9","article-title":"q-Bernoulli numbers and polynomials","volume":"15","author":"Carlitz","year":"1948","journal-title":"Duke Math. 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