Rong-Hua Wang

activity

20242026

collaborators

6 papers

math.CO2026

Polynomial reduction for $q$ -holonomic sequences

Rong-Hua Wang, Xiao-Ran Yang, Michael X. X. Zhong

This paper provides a (Laurent) polynomial reduction to $q$ -holonomic sequences $F_{k} (q)$ . We first characterize Laurent polynomials $p ~ (x)$ such that the product $\tilde{p}(…

math.NT2025

$q$ -Congruences for Z.-W. Sun's generalized polynomials $w_{k}^{(α)} (x)$

Lin-Yue Li, Rong-Hua Wang

In 2022, Z.-W. Sun defined \begin{equation*} w_k^{(α)}{(x)}=\sum_{j=1}^{k}w(k,j)^αx^{j-1}, \end{equation*} where $k, α$ are positive integers and $w(k,j)=\frac{1}{j}\binom{k-1}{j-1}…

math.CO2025

Congruences for sums of Delannoy numbers and polynomials

Rong-Hua Wang, Michael X. X. Zhong

In this paper, we apply the power-partible reduction to study arithmetic properties of sums involving Delannoy numbers $D_{k}$ and polynomials $D_{k} (z)$ . Let $v\in\bN$ and $p$ be an o…

math.NT2025

Arithmetic properties of generalized Delannoy polynomials and Schröder polynomials

Lin-Yue Li, Rong-Hua Wang

Let $n$ be any nonnegative integer and \[ D_n^{(h)}(x)=\sum_{k=0}^{n}\binom{n+k}{2k}^{h}\binom{2k}{k}^{h}{x}^{k} \text{ and } S_{n}^{(h)}(x)=\sum_{k=0}^{n}\binom{n+k}{2k}^{h}C_{k}^…

math.NT2024

On an Erdős-type conjecture on $F_{q} [x]$

Rongyin Wang

P. Erdős conjectured in 1962 that on the ring $Z$ , every set of $n$ congruence classes in $Z$ that covers the first $2^{n}$ positive integers also covers the ring $…

math.CO2024

Rational reductions for holonomic sequences

Rong-Hua Wang

Given a holonomic sequence $F (n)$ , we characterize rational functions $r (n)$ so that $r (n) F (n)$ can be summable. We provide upper and lower bounds on the degree of the numerator of…

Polynomial reduction for q-holonomic sequences

q-Congruences for Z.-W. Sun's generalized polynomials wk(α)​(x)