L. Sun

activity

20172026

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4 papers · 1 filter

math.CO2026

A combinatorial proof for the positivity of the normalized Jacobi triple product tails

Xiangyu Ding, Lisa Hui Sun

For $k \geq 1$ , we prove that \[ [q^n z^s]J_k(z,q)\geq 0, \qquad (n\geq 0,\ s\in\mathbb Z) \] for the normalized Jacobi triple product tails \[ J_k(z,q) = \frac{ \sum_{j=k}^{\infty}…

math.CO2025

Bilateral Bailey pairs and Rogers-Ramanujan type identities

Xiangxin Liu, Lisa Hui Sun

Rogers-Ramanujan type identities occur in various branches of mathematics and physics. As a classic and powerful tool to deal with Rogers-Ramanujan type identities, the theory of B…

math.CO2024

Truncated theta series from the Bailey lattice

Xiangyu Ding, Lisa Hui Sun

In 2012, Andrews and Merca obtained a truncated version of Euler's pentagonal number theorem and showed the nonnegativity related to partition functions. Meanwhile, Andrews-Merca a…

math.CO2017

On the Enumeration and Congruences for m-ary Partitions

Lisa Hui Sun, Mingzhi Zhang

Let $m \geq 2$ be a fixed positive integer. Suppose that $m^{j} \leq n < m^{j + 1}$ is a positive integer for some $j \geq 0$ . Denote $b_{m} (n)$ the number of $m$ -ary partitions of $n$ , whe…