11 citations · 27 across the 12 of their papers we have counts for
15 papers
Rhoban Football Club: RoboCup Humanoid Kid-Size 2023 Champion Team Paper
Julien Allali, Adrien Boussicault, Cyprien Brocaire +8
In 2023, Rhoban Football Club reached the first place of the KidSize soccer competition for the fifth time, and received the best humanoid award. This paper presents and reviews im…
Baxter Tree-like Tableaux
Jean-Christophe Aval, Adrien Boussicault, Mathilde Bouvel +2
Tree-like tableaux are objects in bijection with alternative or permutation tableaux. They have been the subject of a fruitful combinatorial study for the past few years. In the pr…
Non-ambiguous trees: new results and generalisation (Full version)
Bérénice Delcroix-Oger, Florent Hivert, Patxi Laborde-Zubieta +2
We present a new definition of non-ambiguous trees (NATs) as labelled binary trees. We thus get a differential equation whose solution can be described combinatorially. This yields…
Generating series of Periodic Parallelogram polyominoes
Jean Christophe Aval, Adrien Boussicault, Patxi Laborde-Zubieta +1
The aim of this work is the study of the class of periodic parallelogram polyominoes, and two of its variantes. These objets are related to 321-avoiding affine permutations. We fir…
Periodic Parallelogram Polyominoes
Adrien Boussicault, Patxi Laborde-Zubieta
A periodic parallelogram polyomino is a parallelogram polyomino such that we glue the first and the last column. In this work we extend a bijection between ordered trees and parall…
Non-ambiguous trees: new results and generalisation
Jean-Christophe Aval, Adrien Boussicault, Berenice Delcroix-Oger +2
We present a new definition of non-ambiguous trees (NATs) as labelled binary trees. We thus get a differential equation whose solution can be described combinatorially. This yield…
The number of directed k-convex polyominoes
Adrien Boussicault, Simone Rinaldi, Samanta Socci
We present a new method to obtain the generating functions for directed convex polyominoes according to several different statistics including: width, height, size of last column/r…
Combinatorics of non-ambiguous trees
Jean-Christophe Aval, Adrien Boussicault, Mathilde Bouvel +1
This article investigates combinatorial properties of non-ambiguous trees. These objects we define may be seen either as binary trees drawn on a grid with some constraints, or as a…
The tree structure in staircase tableaux
Jean-Christophe Aval, Adrien Boussicault, Sandrine Dasse-Hartaut
Staircase tableaux are combinatorial objects which appear as key tools in the study of the PASEP physical model. The aim of this work is to show how the discovery of a tree structu…
Tree-like tableaux
Jean-Christophe Aval, Adrien Boussicault, Philippe Nadeau
In this work we introduce and study tree-like tableaux, which are certain fillings of Ferrers diagrams in simple bijection with permutation tableaux and alternative tableaux. We ex…
Linear extension sums as valuations of cones
Adrien Boussicault, Valentin Feray, Alain Lascoux +1
The geometric and algebraic theory of valuations on cones is applied to understand identities involving summing certain rational functions over the set of linear extensions of a po…
Application of graph combinatorics to rational identities of type A
Adrien Boussicault, Valentin Féray
To a word , we associate the rational function . The main object, introduced by C. Greene to generalize identities linked to Murnaghan-…
Hyperdeterminantal computation for the Laughlin wave function
Adrien Boussicault, Jean-Gabriel Luque, Christophe Tollu
The decomposition of the Laughlin wave function in the Slater orthogonal basis appears in the discussion on the second-quantized form of the Laughlin states and is straightforwardl…
Staircase Macdonald polynomials and the -Discriminant
Adrien Boussicault, Jean-Gabriel Luque
We prove that a -deformation $\Disc k\X q$ of the powers of the discriminant is equal, up to a normalization, to a specialization of a Macdonald polynomial indexed by a staircas…
Hankel hyperdeterminants, rectangular Jack polynomials and even powers of the Vandermonde
Hacene Belbachir, Adrien Boussicault, Jean-Gabriel Luque
We investigate the link between rectangular Jack polynomials and Hankel hyperdeterminants. As an application we give an expression of the even power of the Vandermonde in term of J…