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

[摘要] 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 generating function of $b(n,1)$. We give a proof of

[学科分类] 离散数学和组合数学

[关键词] partition;hook length;nearly $k$-triangular partition