Permutations with Confined Displacements

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Abstract
A fundamental problem in combinatorial analysis is the classification of the permutations of 1, 2, …, n which satisfy a system of constraints. Thus one may ask such questions as how many permutations are there which have exactly r k-cycles; how many have at least s cycles regardless of cycle length. Again, one may ask how many permutations are there in which k ascending sequences appear; or how many permutations are there in which specified numbers may not appear in specified places or at specified distances from other numbers. The literature on these problems is quite extensive. References [1,2,5,7,10,14,17] give an indication of the present, status of these problems.

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