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Derangements on a Ferrers board. (English) Zbl 1325.05012

Summary: We study the derangement number on a Ferrers board \(B = (n \times n) - \lambda\) with respect to an initial permutation \(M\), that is, the number of permutations on \(B\) that share no common points with \(M\). We prove that the derangement number is independent of \(M\) if and only if \(\lambda\) is of rectangular shape. We characterize the initial permutations that give the minimal and maximal derangement numbers for a general Ferrers board, and present enumerative results when \(\lambda\) is a rectangle.

MSC:

05A05 Permutations, words, matrices
05A18 Partitions of sets
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References:

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