Derangements in a Ferrers Board
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The classic derangement question of counting the number of derangements for n objects from some initial permutation of the objects was first considered by de Montfort in 1708. A particular recasting of a permutation allows us to place any permutation onto an n x n board, from which certain properties of derangements may be understood. This research extends the classic derangement question to the more general Ferrers board, which is an n x n board with a missing section in the lower-right corner. Various properties of the derangement numbers for these more general boards are stated and proven in the course of this work.
Linz, William B (2014). Derangements in a Ferrers Board. Undergraduate Research Scholars Program. Available electronically from