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Applied Mathematics and Computation, ISSN 0096-3003, 06/2013, Volume 219, Issue 19, pp. 9978 - 9991
We discuss the generalized Touchard polynomials introduced recently by Dattoli et al. as well as their extension to negative order introduced by the authors... 
Bell number | Generating function | Stirling number | Touchard polynomial | MATHEMATICS, APPLIED
Journal Article
Journal of Number Theory, ISSN 0022-314X, 08/2017, Volume 177, pp. 136 - 152
In the present article we extend several arithmetical results to a family of generalized Bell numbers called r-Bell numbers. In particular, we generalize some... 
p-adic valuation | r-Bell numbers | r-Stirling numbers | Touchard's congruence | MODULO | STIRLING NUMBERS | SET PARTITIONS | CONGRUENCES | MATHEMATICS | PRIME | PERIOD | LARGEST SINGLETONS | CLASSICAL UMBRAL CALCULUS | Information science | Statistics | Analysis
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 02/2012, Volume 218, Issue 12, pp. 6661 - 6665
The theory of Touchard polynomials is generalized using a method based on the definition of exponential operators, which extend the notion of the shift... 
Stirling numbers | Exponential operators | Touchard polynomials | MATHEMATICS, APPLIED | Derivation | Operators | Mathematical models | Computation | Mathematical analysis | Formalism
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 03/2015, Volume 254, pp. 204 - 209
We consider the real-rootedness of generalized Touchard polynomials recently revisited by Mansour and Schork (2013). Towards this end, we first describe the... 
Real-rootedness | Alternating | Interlacing | Generalized Touchard polynomials | Generalized touchard polynomials | MATHEMATICS, APPLIED
Journal Article
Indagationes Mathematicae, ISSN 0019-3577, 08/2015, Volume 26, Issue 4, pp. 634 - 645
A q-deformed analog of the generalized Touchard polynomials is considered and the connection to generalized Stirling numbers and Bell polynomials is... 
Touchard polynomials, Generalized Stirling numbers, [formula omitted]-deformation, Spivey relation | Spivey relation | Touchard polynomials | Generalized Stirling numbers | q-deformation | Q-ANALOG | MATHEMATICS | UNIFIED APPROACH
Journal Article
Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 2011, Volume 118, Issue 1, pp. 9 - 26
Two well-known q-Hermite polynomials are the continuous and discrete q-Hermite polynomials. In this paper we consider a new family of q-Hermite polynomials and... 
Matchings | q-Hermite polynomials | Hankel determinants | Touchard–Riordan formula | Al-Salam–Chihara polynomials | Hermite polynomials | Catalan numbers | Q-Hermite polynomials | Touchard-Riordan formula | Al-Salam-Chihara polynomials | MATHEMATICS | NUMBERS | FORMULA
Journal Article
Electronic Communications in Probability, ISSN 1083-589X, 2017, Volume 22
We present a new proof of a fundamental result concerning cycles of random permutations which gives some intuition for the connection between Touchard... 
Cycles in random permutations | Dobínski’s formula | Touchard polynomials | Bell numbers | Permutations that fix a set | Ewens sampling distribution | Covers of multisets | covers of multisets | formula | STATISTICS & PROBABILITY | Dobinski's | permutations that fix a set | cycles in random permutations
Journal Article
by Yan, HR and Zhang, QL and Xu, AM
JOURNAL OF MATHEMATICAL INEQUALITIES, ISSN 1846-579X, 09/2019, Volume 13, Issue 3, pp. 645 - 653
A unified generalization for the Bell-Touchard polynomials of order k and the r-Bell polynomials is established. It is shown that the generating function of... 
logarithmic convexity | MATHEMATICS | inequality | MATHEMATICS, APPLIED | 1ST | Bell-Touchard polynomial | absolutely monotonic | EQUATIONS | completely monotonic | WEIGHTED STIRLING NUMBERS
Journal Article
Open Mathematics, ISSN 2391-5455, 01/2016, Volume 14, Issue 1, pp. 908 - 912
In this paper, we present differential equation for the generating function of the , -Touchard polynomials. An application to ordered partitions of a set is... 
llB47 | Ordered partitions | llB48 | Touchard polynomials | Exponential polynomials | 05A48 | 05A18 | MATHEMATICS | IDENTITIES | Functions, Exponential | Theorems (Mathematics) | Usage | Polynomials | Differential equations | Tests, problems and exercises
Journal Article
Mathematica Æterna, ISSN 1314-3336, 11/2016, Volume 6, Issue 5, pp. 765 - 779
Journal Article
Advanced Studies in Contemporary Mathematics (Kyungshang), ISSN 1229-3067, 01/2015, Volume 25, Issue 1, pp. 39 - 46
Journal Article
Advanced Studies in Contemporary Mathematics (Kyungshang), ISSN 1229-3067, 2017, Volume 27, Issue 2, pp. 243 - 251
Journal Article
Communications in Statistics - Theory and Methods, ISSN 0361-0926, 04/2019, Volume 48, Issue 8, pp. 2049 - 2059
Journal Article
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