Geodesic
Bijection between increasing binary trees and rook placements on double staircases
Bishal Deb1
1University College London
The electronic journal of combinatorics, Tome 30 (2023) no. 1
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In this paper, we shall construct a bijection between rook placements on double staircases (introduced by Josuat-Vergès in 2017) and increasing binary trees. We introduce two subclasses of rook placements on double staircases, which we call left and right-aligned rook placements. We show that their enumeration, while keeping track of a certain statistic, gives the $\gamma$-vectors of the Eulerian polynomials. We conclude with a discussion on a different bijection that fits in very well with our main bijection, and another discussion on generalising our main bijection. Our main bijection is a special case of a bijection due to Tewari (2019).
DOI : 10.37236/10926
Classification : 05E10, 05A19, 05C05, 05A05
Mots-clés : Young's lattice, tableaux, growth diagrams, Dyck paths

Bishal Deb  1

1 University College London 
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Bishal Deb. Bijection between increasing binary trees and rook placements on double staircases. The electronic journal of combinatorics, Tome 30 (2023) no. 1. doi: 10.37236/10926

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