The Baxter permutations who are alternating and whose inverse is also alternating are shown to be enumerated by the Catalan numbers. A bijection to complete binary trees is also given. © 2000 Elsevier Science B.V. All rights reserved.
Guibert, O., & Linusson, S. (2000). Doubly alternating Baxter permutations are Catalan. Discrete Mathematics, 217(1–3), 157–166. https://doi.org/10.1016/S0012-365X(99)00261-7