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Séminaire Lotharingien de Combinatoire, 85B.47 (2021), 12 pp.

# Cyril Banderier and Michael Wallner

# Young Tableaux with Periodic Walls: Counting with the Density Method

**Abstract.**
We consider a generalization of Young tableaux
in which we allow some consecutive pairs of cells with decreasing labels,
conveniently visualized by a "wall" between the corresponding cells.
Some shapes can be enumerated by variants of hook-length type formulas.
We focus on families of tableaux (like the so-called "Jenga tableaux")
having some periodic shapes,
for which the generating functions are harder to obtain.
We get some interesting new classes of recurrences,
and a surprisingly rich zoo of generating functions
(algebraic, hypergeometric, D-finite, differentially-algebraic).
Some patterns lead to nice bijections with trees, lattice paths, or permutations.
Our approach relies on the density method, a powerful way to perform both random generation
and enumeration of linear extensions of posets.

Received: December 1, 2020.
Accepted: March 1, 2021.
Final version: April 29, 2021.

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