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

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

2005-06-14

arxiv.org/abs/math/0506274v1

Mathematics

Combinatorics

15 pages

Scientific paper

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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