5 citations · 13 across the 8 of their papers we have counts for
8 papers
Entanglement from Expansion: High Rank-Width in Deterministic Graphs
Tristan Cam, Cyril Gavoille, Yvan Le Borgne +1
Entanglement in quantum graph states is intrinsically linked to rank-width, a graph complexity measure introduced by Oum and Seymour. In this work, we enable the preparation of max…
The sandpile model on the complete split graph: -Schröder polynomials, sawtooth polyominoes, and a cycle lemma
Henri Derycke, Mark Dukes, Yvan Le Borgne
This paper studies sorted recurrent configurations of the Abelian sandpile model on the complete split graph. We introduce two natural toppling processes, CTI and ITC toppling, on…
Shuffle theorems and sandpiles
Michele D'Adderio, Mark Dukes, Alessandro Iraci +3
We provide an explicit description of the recurrent configurations of the sandpile model on a family of graphs , which we call clique-independent graphs, indexed…
Tiered trees and Theta operators
Michele D'Adderio, Alessandro Iraci, Yvan LeBorgne +2
In [Dugan-Glennon-Gunnells-Steingrimsson-2019], the authors introduce tiered trees to define combinatorial objects counting absolutely indecomposable representations of certain qui…
Asymptotic behaviour of the one-dimensional "rock-paper-scissors" cyclic cellular automaton
Benjamin Hellouin de Menibus, Yvan Le Borgne
The one-dimensional three-state cyclic cellular automaton is a simple spatial model with three states in a cyclic "rock-paper-scissors" prey-predator relationship. Starting from a…
The sandpile model on K_{m,n} and the rank of its configurations
Michele D'Adderio, Yvan Le Borgne
We present an algorithm to compute the rank of a configuration of the sandpile model for the complete bipartite graph K_{m,n} of complexity O(m+n). Furthermore, we provide a formul…
The Riemann-Roch theorem for graphs and the rank in complete graphs
Robert Cori, Yvan Le Borgne
The paper by M. Baker and S. Norine in 2007 introduced a new parameter on configurations of graphs and gave a new result in the theory of graphs which has an algebraic geometry fla…
Two operators on sandpile configurations, the sandpile model on the complete bipartite graph, and a Cyclic Lemma
Jean-Christophe Aval, Michele D'Adderio, Mark Dukes +1
We introduce two operators on stable configurations of the sandpile model that provide an algorithmic bijection between recurrent and parking configurations. This bijection preserv…