On the poset of King-Non-Attacking permutations

Abstract

A king-non-attacking permutation is a permutation $\pi \in S_n$ such that $|\pi (i)-\pi (i-1)|\ne 1$ for each $i\in \{2,\dots ,n\}$. We investigate the structure of the poset of these permutations under the containment relation, and also provide some results on its Möbius function.