Combinatorics / CONCEPT

Insertion before the minimum when the maximum is second

Let p be a permutation of size n at least four with maximum second. In the suffix after its first two entries, values above its first entry a decrease, and no value below a has both a smaller and a larger such value later. Assume no adjacent entries have consecutive values, the minimum has zero-based position k at least two, and p is neither P(floor(n/2)) nor E(floor(n/2)). If k is even choose rank a minus k/2 plus one; otherwise choose rank n minus (k-1)/2 plus one. Increase all values at least that rank and insert it before the minimum. The result is a simple permutation in C with maximum second, minimum at position k + 1, and outside the same two families. Deleting the inserted entry and standardizing recovers p.