A Class of Combinatorial Functions for Eulerian Numbers (MATEMATIKA, 2012)
In this note, we introduce a new class of functions pertaining to binomial coefficients $\binom{n}{m}$ and Eulerian numbers $\left < \! \begin{array}{c} n \\ m \end{array} \!\right}$ which arise in the recent study of descents in permutations. Given positive integers $a$ and $b$, let $f_i(x) = 2^{−i} \binom{a+b}{i} \left