Combinatorial Interpretations of the q-Faulhaber and q-Salie Coefficients

2005/06/14 by Guo, Victor J. W., Rubey, Martin, Zeng, Jiang
#05A30 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.math/0506274

Abstract

Recently, Guo and Zeng discovered two families of polynomials featuring in a q-analogue of Faulhaber's formula for the sums of powers and a q-analogue of Gessel-Viennot's formula involving Salie's coefficients for the alternating sums of powers. In this paper, we show that these are polynomials with symmetric, nonnegative integral coefficients by refining Gessel-Viennot's combinatorial interpretations.

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