32 citations · 140 across the 26 of their papers we have counts for
3 papers · 1 filter
Dynamics of Non-polar Solutions to the Discrete Painlevé I Equation
Nicholas Ercolani, Joceline Lega, Brandon Tippings
This manuscript develops a novel understanding of non-polar solutions of the discrete Painlevé I equation (dP1). As the non-autonomous counterpart of an analytically completely int…
A Path-Counting Analysis of Phase Shifts in Box-Ball Systems
Nicholas M. Ercolani, Jonathan Ramalheira-Tsu
In this paper, we perform a detailed analysis of the phase shift phenomenon of the classical soliton cellular automaton known as the box-ball system, ultimately resulting in a stat…
The Ghost-Box-Ball System: A Unified Perspective on Soliton Cellular Automata, the RSK Algorithm and Phase Shifts
Nicholas M. Ercolani, Jonathan Ramalheira-Tsu
In this paper, we introduce the ghost-box-ball system, which is an extended version of the classical soliton cellular automaton. It is initially motivated as a mechanism for making…