On the Permutations that Strongly Avoid the Pattern 312 or 231.

In 2019, Bóna and Smith introduced the notion of strong pattern avoidance for which a permutation and its square both avoid a given pattern. In this paper, we enumerate the set of permutations π which not only strongly avoid the pattern 312 or 231 but also avoid the pattern τ , for all τ ∈ S 3 and some τ ∈ S 4 . One of these results gives a positive answer to a conjecture of Archer and Geary. [ABSTRACT FROM AUTHOR]