Showing math.COShow all
2 papers · 1 filter
math.CO2026
A combinatorial proof for the positivity of the normalized Jacobi triple product tails
Xiangyu Ding, Lisa Hui Sun
For , 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.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…