TITLE:
A Relationship between the Partial Bell Polynomials and Alternating Run Polynomials
AUTHORS:
Yanan Feng, Zhe Wang
KEYWORDS:
Alternating Run Polynomials, Bell Polynomials, Permutations
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.13 No.2,
April
28,
2023
ABSTRACT: In this
note, we first derive an exponential generating function of the alternating run
polynomials. We then deduce an explicit formula of the alternating run
polynomials in terms of the partial Bell polynomials.