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arXiv · 1803.03086

Topological Degree of Shift Spaces on Monoids

Jung-Chao Ban·Chih-Hung Chang·Nai-Zhu Huang
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Abstract

This paper considers the topological degree of $G$-shifts of finite type for the case where $G$ is a nonabelian monoid. Whenever the Cayley graph of $G$ has a finite representation and the relationships among the generators of $G$ are determined by a matrix $A$, the coefficients of the characteristic polynomial of $A$ are revealed as the number of children of the graph. After introducing an algorithm for the computation of the degree, the degree spectrum, which is finite, relates to a collection of matrices in which the sum of each row of every matrix is bounded by the number of children of the graph. Furthermore, the algorithm extends to $G$ of finite free-followers.

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Jung-Chao Ban, Chih-Hung Chang, Nai-Zhu Huang. 2018-03-08. Topological Degree of Shift Spaces on Monoids. https://arxiv.org/abs/1803.03086

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