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arXiv · 1710.07007

Quarter-Turn Baxter Permutations

Kevin Dilks
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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 $q=-1$ 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.

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Kevin Dilks. 2017-10-19. Quarter-Turn Baxter Permutations. https://arxiv.org/abs/1710.07007

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