Abstract
Cayley graphs of monoids defined through special confluent rewriting systems are known to be hyperbolic metric spaces which admit a compact completion given by irreducible finite and infinite words. In this paper, we prove that the fixed point submonoids for endomorphisms of these monoids which are boundary injective (or have bounded length decrease) are rational, with similar results holding for infinite fixed points. Decidability of these properties is proved, and constructibility is proved for the case of bounded length decrease. These results are applied to free products of cyclic groups, providing a new generalization for the case of infinite fixed points.
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Communicated by J. Wilson.
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Silva, P.V. Fixed points of endomorphisms over special confluent rewriting systems. Monatsh Math 161, 417–447 (2010). https://doi.org/10.1007/s00605-009-0124-0
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DOI: https://doi.org/10.1007/s00605-009-0124-0