On a periodic soliton cellular automaton

Abstract

We propose a box and ball system with a periodic boundary condition (pBBS).\nThe time evolution rule of the pBBS is represented as a Boolean recurrence\nformula, an inverse ultradiscretization of which is shown to be equivalent with\nthe algorithm of the calculus for the 2Nth root. The relations to the pBBS of\nthe combinatorial R matrix of ${U'}_q(A_N^{(1)})$ are also discussed.\n