Br\"and\'en's $(p,q)$-Eulerian polynomials, Andr\'e permutations and continued fractions

20 Mar 2020 Pan Qiong Qiong Zeng Jiang

In 2008 Br\"and\'en proved a $(p,q)$-analogue of the $\gamma$-expansion formula for Eulerian polynomials and conjectured the divisibility of the $\gamma$-coefficient $\gamma_{n,k}(p,q)$ by $(p+q)^k$. As a follow-up, in 2012 Shin and Zeng showed that the fraction $\gamma_{n,k}(p, q)/(p + q)^k$ is a polynomial in $\N[p,q]$... (read more)

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