On hook length biases in $t$-regular partitions

Rupam Barman, Pankaj Jyoti Mahanta, Gurinder Singh

Let $t\ge 2$ and $k\ge 1$ be integers. A $t$-regular partition of a positive integer $n$ is a partition of $n$ such that none of its parts is divisible by $t$. Let $b_{t,k}(n)$ den…