3 problems

Let $P=\{P_n(x)\}_{n\geq 0}$ be a polynomial sequence with $\deg(P_n(x))=n$, and write … The associated Eulerian transformation is the linear transformation obtained by taking…

Let $R_0=(\binom{n}{k})_{n,k=0}^{\infty}$, and let $\mathcal{A}_{R_0}$ be the associated Chow-Eulerian map. For a polynomial $f$, say that $f$ has a nonnegative expansion in the ba…

Let $f$ be an irreducible polynomial over $\mathbb F_q$ of degree $n\ge 3$, and let $Q_c$ be a polynomial of degree $D$. Suppose that $n$ is odd and $D\equiv 2\pmod 4$, and that th…