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arXiv · 2304.12246

On the determinicity of paths on substitution complexes

I. A. Ivanov-Pogodaev
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Abstract

The paper is devoted to the study of combinatorial determinacy properties of a family of substitution complexes consisting of quadrilaterals glued side-to-side with each other. These properties are useful in constructing algebraic structures with a finite number of defining relations. In particular, this method was used when constructing a finitely presented infinite nisemigroup satisfying the identity x^9 =0. This construction responds to the problem of L. N. Shevrin and M. V. Sapir. In this paper, we investigate the possibility of coloring the entire sequence of complexes into a finite number of colors, in which the property of weak determinism is fulfilled: if the colors of the three vertices of a certain quadrilateral are known, then the color of the fourth side is uniquely determined, except in some cases of a special arrangement of the quadrilateral.

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I. A. Ivanov-Pogodaev. 2023-04-24. On the determinicity of paths on substitution complexes. https://arxiv.org/abs/2304.12246

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