Combinatorics / CONCEPT

An interval crossing a fixed gap

Let p be a non-simple permutation in C such that every proper nontrivial interval crosses a fixed gap strictly and has minimum value greater than one. There is a proper nontrivial interval containing every such interval. Contracting it gives a simple skeleton in C occurring in p, and standardizing its entries gives a block. Inflating that skeleton by this block recovers p. If the block has length m, the skeleton has length equal to the length of p minus m plus one.