Zeilberger introduced a restriction on the positions of the largest elements in a permutation in the process of verifying the conjecture on the number of West-2-stack-sortable permutations. In this paper we look at Zeilberger's restriction combined with the avoidance of classical patterns of length 3. We provide enumeration results as well as bijections to two different types of Dyck paths.
For a permutation 𝜋 = 𝜋1𝜋2...𝜋n, the longest run of largest elements that are in decreasing order in 𝜋, is it's maximal decreasing run.
The permutation 𝜋 = 1746523 has a maximal decreasing run of 3, since 765 is the longest run of largest elements that are in decreasing order.