Topic
Touchard polynomials
About: Touchard polynomials is a research topic. Over the lifetime, 33 publications have been published within this topic receiving 163 citations.
Papers
TL;DR: In this paper, a class of related polynomials is introduced and a combinatorial interpretation is discussed, and an exponential generating function, recurrence relations and connections with other well-known polynomial numbers are obtained.
25 citations
TL;DR: In this paper, the theory of Touchard polynomials is generalized using a method based on the definition of exponential operators, which extend the notion of the shift operator, and the proposed technique, along with the use of the relevant operational formalism, allows the straightforward derivation of properties of this family of polynomial and their relationship to different forms of Stirling numbers.
16 citations
1 Jan 2011
TL;DR: In this paper, the authors established relations between Touchard polynomials, Bell polynomorphisms, and polynomial types of binomial numbers with Stirling numbers.
Abstract: Touchard generalized the Bell polynomials in order to give some combinatorial interpretation on permutations. Chrysaphinou introduced and studied a class of polynomials related to Touchard’s generalization. In the present paper, we establish some relations between Touchard polynomials, Bell polynomials and the polynomials of binomial type. Several identities and relations with Stirling numbers are obtained.
12 citations
TL;DR: The differential equation for the generating function of the p, q-Touchard polynomials is presented and an application to ordered partitions of a set is investigated.
Abstract: Abstract In this paper, we present differential equation for the generating function of the p, q-Touchard polynomials. An application to ordered partitions of a set is investigated.
9 citations
TL;DR: A recursion relation for the generalized Touchard polynomials is established and it is shown that one can interpret some of the resulting formulas as binomial theorems for particular noncommuting variables.
9 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 4 |
| 2020 | 6 |
| 2019 | 5 |
| 2017 | 3 |
| 2016 | 4 |
| 2015 | 3 |