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The number of ways of placing k non-taking rooks on a Ferrers board B n is obtained as a finite difference of order n-k of a polynomial of order n. Then the number of permutations of the set {1,2,...,n} with k elements in restricted positions, when the board of the restricted positions is a Ferrers board B n , is derived as a backward finite difference of order n+1 of a modified polynomial...
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