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

Victor J. W. Guo·Martin Rubey·Jiang Zeng
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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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Victor J. W. Guo, Martin Rubey, Jiang Zeng. 2005-06-14. Combinatorial Interpretations of the q-Faulhaber and q-Salie Coefficients. https://arxiv.org/abs/math/0506274

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