4 problems

For $h,m,n\in\mathbb Z^+$, define the generalized Delannoy polynomials … and the generalized Schröder polynomials … where $C_k=\binom{2k}{k}/(k+1)$ and $(a,b,c)$ denotes the greate…

Let $D_k(x)$ be the Delannoy polynomial, defined by … Let $x$ be an integer and let $p$ be an odd prime. The mod-$p^3$ refinement. … The paper proves the corresponding congruence m…

Let $D_k(x)$ be the Delannoy polynomial, defined by … For a prime $p$, let $\nu_p$ denote the $p$-adic valuation. Let $n$ be a positive integer and let $x$ be a $p$-adic integer. Z…

Let $n$ and $m$ be positive integers, and let … be the central Delannoy polynomial. Sun's conjecture. … is always an integer. This asserts integrality of the normalized sum of powe…