About: Baxter permutation

In combinatorial mathematics, a Baxter permutation is a permutation which satisfies the following generalized pattern avoidance property: * There are no indices i < j < k such that σ(j + 1) < σ(i) < σ(k) < σ(j) or σ(j) < σ(k) < σ(i) < σ(j + 1). Equivalently, using the notation for vincular patterns, a Baxter permutation is one that avoids the two dashed patterns 2-41-3 and 3-14-2. For example, the permutation σ = 2413 in S4 (written in one-line notation) is not a Baxter permutation because, taking i = 1, j = 2 and k = 4, this permutation violates the first condition.