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Let α k (λ) denote the number of k-hooks in a partition λ and let b(n, k) be the maximum value of α k (λ) among partitions of n. Amdeberhan posed a conjecture on the generating function of b(n, 1). We give a proof of this conjecture. In general, we obtain a formula that can be used to determine b(n, k). This leads to a generating function formula for b(n,… (More)

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