3 papers
cs.DM2026
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…
math.CO2024
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…
math.CO2024
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…