English

Quarter-Turn Baxter Permutations

Combinatorics 2017-10-20 v1

Abstract

Baxter permutations are known to be in bijection with a wide number of combinatorial objects. Previously, it was shown that each of these objects had a natural involution which was carried equivariantly by the known bijections, and the number of objects fixed under involution was given by Stembridge's q=1q=-1 phenomenon. In this paper, we consider the order 4 action of a quarter-turn rotation of a Baxter permutation matrix, refining the half-turn rotation previously studied. Using the method of generating trees, we show that the number of Baxter permutations fixed under quarter-turn rotation has a very nice enumeration, which suggests the existence of a combinatorial bijection.

Keywords

Cite

@article{arxiv.1710.07007,
  title  = {Quarter-Turn Baxter Permutations},
  author = {Kevin Dilks},
  journal= {arXiv preprint arXiv:1710.07007},
  year   = {2017}
}

Comments

14 pages, 13 figures

R2 v1 2026-06-22T22:18:57.693Z