Congruences Relating Regular Partition Functions, a Genearalised Tau Function and Partition Function Weighted Composition Sums

S. Sriram, A. David Christopher

Let $n$ and $t$ be positive integers with $t\ge 2$. Let $R_t(n)$ be the number of $t$-regular partitions of $n$. A class of functions, denoted $\ddot{I}{„}_k(n)$, is defined as follows: \[…