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arxiv: 1009.5167 · v2 · pith:ECHAI4BVnew · submitted 2010-09-27 · 🧮 math.CO · cs.DM

Combinatorial substitutions and sofic tilings

Thomas Fernique (LIF) , Nicolas Ollinger (LIF) This is my paper
classification 🧮 math.CO cs.DM
keywords tilingscombinatorialsetssoficallowsconstraintsdefineenforced
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A combinatorial substitution is a map over tilings which allows to define sets of tilings with a strong hierarchical structure. In this paper, we show that such sets of tilings are sofic, that is, can be enforced by finitely many local constraints. This extends some similar previous results (Mozes'90, Goodman-Strauss'98) in a much shorter presentation.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Matching Rules for Substitution and Hierarchical Tilings for any Substitution with Finite Local Complexity

    math.DS 2026-06 unverdicted novelty 7.0

    Any substitution with finite local complexity yields substitution tilings and hierarchical tilings that admit local matching rules.