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arXiv · 1210.2618

Enumeration of fixed points of an involution on $β(1,0)$-trees

Sergey Kitaev·Anna de Mier
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Abstract

$β(1,0)$-trees provide a convenient description of rooted non-separable planar maps. The involution $h$ on $β(1,0)$-trees was introduced to prove a complicated equidistribution result on a class of pattern-avoiding permutations. In this paper, we describe and enumerate fixed points of the involution $h$. Intriguingly, the fixed points are equinumerous with the fixed points under taking the dual map on rooted non-separable planar maps, even though the fixed points do not go to each other under the know (natural) bijection between the trees and the maps.

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Sergey Kitaev, Anna de Mier. 2012-10-09. Enumeration of fixed points of an involution on $β(1,0)$-trees. https://arxiv.org/abs/1210.2618

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