Derivative polynomials and permutations by numbers of interior peaks and left peaks
Combinatorics
2011-11-28 v2
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.
Keywords
Cite
@article{arxiv.1106.5781,
title = {Derivative polynomials and permutations by numbers of interior peaks and left peaks},
author = {Shi-Mei Ma},
journal= {arXiv preprint arXiv:1106.5781},
year = {2011}
}
Comments
12 pages