TY - JOUR
AU - Ramalheira-Tsu, Jonathan
AB - Abstract: 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 precise a connection between the Schensted insertion (of the Robinson-Schensted-Knuth correspondence) and the dynamical process of the box-ball system. In addition to this motivation, we explore generalisations of classical notions of the box-ball system, including the solitonic phenomenon, the asymptotic sorting property, and the invariant shape construction. We analyse the ghost-box-ball system beyond its initial relevance to the Robinson-Schensted-Knuth correspondence, unpacking its relationship to its underlying dynamical evolution on a coordinatisation and using a mechanism for augmenting a regular box-ball configuration to study the classical ultradiscrete phase shift phenomenon.
TI - The Ghost-Box-Ball System: A Unified Perspective on Soliton Cellular Automata, the RSK Algorithm and Phase Shifts
JF - Nonlinear Sciences
DA - 2021-01-19
UR - https://www.deepdyve.com/lp/arxiv-cornell-university/the-ghost-box-ball-system-a-unified-perspective-on-soliton-cellular-IjKjSxEXTl
VL - 2021
IS - 2101
DP - DeepDyve
ER -