Duality between box-ball systems of finite box and/or carrier capacity

2019/05/01 by David A. Croydon, Croydon, David A., Makiko Sasada +1 · 1 citation
Computer Science · Engineering · #37B15 (primary) #60G50 #60K35 #82B99 (secondary) #Cellular Automata and Applications #Coding theory and cryptography #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1905.00189

openalex publication_date 2019/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We construct the dynamics of the box-ball system with box capacity J and carrier capacity K, which we abbreviate to BBS(J,K), in the case of infinite initial configurations, and show that this system is dual to the analogous BBS(K,J) model. Towards this end, we build on previous work for the original box-ball system, that is BBS(1,∞), to show that when the box capacity J and carrier capacity K satisfy J

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