Touchard Polynomials, Partial Bell Polynomials and Polynomials of Binomial Type

摘要

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.