Journal of Integer Sequences, Vol. 14 (2011), Article 11.3.1

Touchard Polynomials, Partial Bell Polynomials and Polynomials of Binomial Type

Miloud Mihoubi and Mohammed Said Maamra
University of Science and Technology Houari Boumediene (USTHB)
Faculty of Mathematics
PB 32
El Alia, 16111, Algiers


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.

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Received October 21 2010; revised version received February 13 2011. Published in Journal of Integer Sequences, March 25 2011.

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