Rational Gluing in Edge Replacement Systems
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916658443976704 |
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| author | Perego, Davide Tarocchi, Matteo |
| author_facet | Perego, Davide Tarocchi, Matteo |
| contents | In this paper, we prove the rationality of the gluing relation of edge replacement systems, which were introduced for studying rearrangement groups of fractals. More precisely, we describe an algorithmic procedure for building a finite state automaton that recognizes pairs of equivalent sequences that are glued in the fractal. This fits in recent interest towards the rationality of gluing relations on totally disconnected compact metrizable spaces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_09276 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rational Gluing in Edge Replacement Systems Perego, Davide Tarocchi, Matteo Group Theory Metric Geometry 20F65 (Primary), 28A80, 68Q45, 37B10, 51F99 (Secondary) In this paper, we prove the rationality of the gluing relation of edge replacement systems, which were introduced for studying rearrangement groups of fractals. More precisely, we describe an algorithmic procedure for building a finite state automaton that recognizes pairs of equivalent sequences that are glued in the fractal. This fits in recent interest towards the rationality of gluing relations on totally disconnected compact metrizable spaces. |
| title | Rational Gluing in Edge Replacement Systems |
| topic | Group Theory Metric Geometry 20F65 (Primary), 28A80, 68Q45, 37B10, 51F99 (Secondary) |
| url | https://arxiv.org/abs/2403.09276 |