Wenston J. T. Zang

activity

20092026

most citedUnimodality of the Andrews-Garvan-Dyson cranks of partitions

7 citations · 13 across the 15 of their papers we have counts for

collaborators

18 papers

math.CO2026

Typical intersecting families are trivial

Yandong Bai, Haoyun Gu, Wenston J. T. Zang

We study the counting problem for non-uniform intersecting families in extremal set theory. Let $J (n, k)$ denote the number of intersecting families $F \subset 2^{[n]}$ suc…

math.CO2025

Proof of Singh and Barman's conjecture on hook length biases

Hongshu Lin, Wenston J. T. Zang

Let $b_{t, i} (n)$ denote the total number of $i$ -hooks in $t$ -regular partitions of $n$ . Singh and Barman conjectured that $b_{t + 1, 2} (n) \geq b_{t, 2} (n)$ holds for all $t \geq 3$ and…

math.CO2025

Generalizations of Euler's Theorem to $k$ -regular partitions

Hongshu Lin, Wenston J. T. Zang

Let $A_{k} (n)$ denote the set of $k$ -distinct partitions of $n$ , and let $B_{k} (n)$ be the set of $k$ -regular partitions of $n$ . Glaisher showed that $# A_{k} (n) = # B_{k} (n)$ . For $k = 2$ …

math.CO2025

New combinatorial proof of Gaussian polynomial and the monotonicity of the Garvan's $k$ -rank

Wenxia Qu, Wenston J. T. Zang

Gaussian polynomial, which is also known as $q$ -binomial coefficient, is one of the fundamental concepts in the theory of partitions. Zeilberger provided a combinatorial proof of G…

math.CO2025

The inequality on the number of $1$ -hooks, $2$ -hooks and $3$ -hooks in $t$ -regular partitions

Hongshu Lin, Wenston J. T. Zang

Let $b_{n, k}$ denote the number of hooks of length $k$ in all the $t$ -regular partitions of $n$ . Singh and Barman raised the question of finding the relation between $b_{t, 2} (n)$ a…

math.CO2025

Bilateral truncated quintuple product

Wenxia Qu, Wenston J. T. Zang

In this paper, we present the bilateral truncated identity of the quintuple product identity, which is a generalization of the truncated quintuple product identities given by Chan,…

Typical intersecting families are trivial

Proof of Singh and Barman's conjecture on hook length biases

Generalizations of Euler's Theorem to k-regular partitions

New combinatorial proof of Gaussian polynomial and the monotonicity of the Garvan's k-rank

The inequality on the number of 1-hooks, 2-hooks and 3-hooks in t-regular partitions

Bilateral truncated quintuple product

Generalizations of Euler's Theorem to $k$ -regular partitions

New combinatorial proof of Gaussian polynomial and the monotonicity of the Garvan's $k$ -rank

The inequality on the number of $1$ -hooks, $2$ -hooks and $3$ -hooks in $t$ -regular partitions