Abstract:In the last few years, a number of authors have proved divisibility properties satisfied by various functions which count the number of overcubic partition $k$--tuples of weight $n$ for small values of $k$. In this work, we use generating functions to prove some of their results as well as multiple infinite families of new congruences for overcubic partition $k$-tuples which do not yet appear in the literature. In particular, we focus on a new perspective which provides insights as to why these functions are often divisible by powers of 2, and we also prove families of congruences whose moduli are odd. For example, we prove that, for all $m\geq 0$, $\OL{b}_{4}(22m + 11) \equiv 0 \pmod{11}$ and we also prove infinite families such as $\OL{b}_{9l+2}(9m+3) \equiv 0 \pmod{3}$ for all $m,l\geq0$.
From: James Sellers [view email]
[v1]
Fri, 19 Jun 2026 22:02:31 UTC (15 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。