On the Maximum Number of k-Hooks of Partitions of n

Anna R. B. Fan, Harold R. L. Yang, Rebecca T. Yu

Let ${\alpha }_k(\lambda )$ denote the number of $k$-hooks in a partition $\lambda$ and let $b(n,k)$ be the maximum value of ${\alpha }_k(\lambda )$ among partitions of $n$. Amdeberhan posed a conjecture on the gener…