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Arithmetic Properties of Partition Quadruples With Odd Parts Distinct (1410.5628v2)
Published 21 Oct 2014 in math.NT and math.CO
Abstract: Let $\mathrm{pod}{-4}(n)$ denote the number of partition quadruples of $n$ where the odd parts in each partition are distinct. We find many arithmetic properties of $\mathrm{pod}{-4}(n)$ involving the following infinite family of congruences: for any integers $\alpha \ge 1$ and $n \ge 0$, [\mathrm{pod}{-4}\Big({{3}{\alpha +1}}n+\frac{5\cdot {{3}{\alpha }}+1}{2}\Big)\equiv 0 \pmod{9}.] We also establish some internal congruences and some congruences modulo 2, 5 and 8 satisfied by $\mathrm{pod}{-4}(n)$.