Combinatorics / CONCEPT

Deleting the first entry of an ordinary continuation

Let q be a simple permutation in C whose minimum has position k at least three and whose second entry is below its maximum. Delete the first entry and decrease each remaining value larger than the deleted value. The resulting permutation p is simple, belongs to C, has its minimum at position k minus one, has its second entry below its maximum, and satisfies W(p) = q. Positions are numbered from zero.