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 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.
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