Baxter Permutations Rise Again

@article{Mallows1979BaxterPR,
  title={Baxter Permutations Rise Again},
  author={Colin L. Mallows},
  journal={J. Comb. Theory, Ser. A},
  year={1979},
  volume={27},
  pages={394-396}
}
Baxter permutations, so named by Boyce, were introduced by Baxter in his study of the fixed points of continuous functions which commute under composition. Recently Chung, Graham, Hoggatt, and Kleiman obtained a sum formula for the number of Baxter permutations of 2n 1 objects, but admit to having no interpretation of the individual terms of this sum. We show that in fact the kth term of this sum counts the number of (reduced) Baxter permutations that have exactly k 1 rises.