Creation of Ballot Sequences in a Periodic Cellular Automaton(General)

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概要

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• 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.

• 社団法人日本物理学会の論文
• 2009-02-15

著者

• Takagi Taichiro

  Department Of Applied Physics National Defense Academy

関連論文

• Higher Spin Cyclic Solid-on-Solid Models
• Vertex Type Fractions of the Six-Vertex Model at Δ=-1
• Creation of Ballot Sequences in a Periodic Cellular Automaton(General)

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