Combinatorics / CONCEPT

Deleting a minimum in the second position

Let q be a permutation in C of size at least four with minimum in its second position, and let p be obtained by deleting that minimum and subtracting one from every remaining entry. Then p is a permutation in C, and shifting its values up by one and reinserting the minimum recovers q. The permutation q is simple if and only if p is simple with minimum not in the second position, or p is the first-entry decreasing inflation of a simple skeleton in C of size at least four, or p equals B at its size.