Combinatorics / CONCEPT

The alternating prefix before the minimum

Let p be a permutation of size n at least four with maximum second, and write a for its first entry. In the suffix after its first two entries, assume values above a decrease and no value below a has both a smaller and a larger such value later. If adjacent entries never have consecutive values and the minimum has zero-based position k, then every entry before k is prescribed: at even position i it equals a minus i/2, and at odd position i it equals n minus floor(i/2).