周期性元胞自动机中选票序列的生成
Creation of ballot sequences in a periodic cellular automaton
摘要：
为了解决一类与晶体基和孤子方程相关的一维周期元胞自动机（CA）的初值问题，我们考虑了初等数学中一个简单命题的推广.最初的命题说，任何字母1和2的序列，不少于1的2的，可以改变成一个投票序列通过循环移位只有。我们将其推广到治疗序列的细胞的共同能力s > 1，其中每个包含连续的2的（左）和1的（右），并表明，这些序列可以改变成一个投票序列通过两个操作，循环和“准循环”的移位。后者是一个新的CA规则，我们发现，在这个规则的时间演化下，各种扭结状结构沿着系统的粒子。
英文摘要：
Motivated by an attempt to develop a method for solving initial value problems in a class of one dimensional periodic cellular automata (CA) associated with crystal bases and soliton equations, we consider a generalization of a simple proposition in elementary mathematics. The original proposition says that any sequence of letters 1 and 2, having no less 1's than 2's, can be changed into a ballot sequence via cyclic shifts only. We generalize it to treat sequences of cells of common capacity s > 1, each of them containing consecutive 2's (left) and 1's (right), and show that these sequences can be changed into a ballot sequence via two manipulations, cyclic and "quasi-cyclic" shifts. The latter is a new CA rule and we find that various kink-like structures are traveling along the system like particles under the time evolution of this rule.
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