Derivative polynomials and permutations by numbers of interior peaks and left peaks

2011/06/27 by Shi-Mei Ma, Ma, Shi-Mei
Mathematics · #05A15 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A15

paper · pdf · doi:10.48550/arxiv.1106.5781

12 pages

arxiv created 2011/11/25 · arxiv updated 2011/11/28

Abstract

Derivative polynomials in two variables are defined by repeated differentiation of the tangent and secant functions. We establish the connections between the coefficients of these derivative polynomials and the numbers of interior and left peaks over the symmetric group. Properties of the generating functions for the numbers of interior and left peaks over the symmetric group, including recurrence relations, generating functions and real-rootedness, are studied.

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