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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.07244 |
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| _version_ | 1866914081802289152 |
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| author | Mućka, A. Romanowska, A. B. |
| author_facet | Mućka, A. Romanowska, A. B. |
| contents | This paper is the second part of a two-part paper investigating the structure and properties of dyadic polygons. A dyadic polygon is the intersection of the dyadic subplane $D^2$ of the real plane $R^2$ and a real convex polygon with vertices in the dyadic plane. Such polygons are described as subreducts (subalgebras of reducts) of the affine dyadic plane $D^2$, or equivalently as commutative, entropic and idempotent groupoids under the binary operation of arithmetic mean. The first part of the paper contained a new classification of dyadic triangles, considered as such groupoids, and a characterization of dyadic triangles with a pointed vertex. This second part investigates isomorphisms of dyadic triangles, and provides a full classification of their isomorphism types. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07244 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometry of dyadic polygons II: isomorphisms of dyadic triangles Mućka, A. Romanowska, A. B. Combinatorics 08A05, 20N02, 52B11, 52A01 This paper is the second part of a two-part paper investigating the structure and properties of dyadic polygons. A dyadic polygon is the intersection of the dyadic subplane $D^2$ of the real plane $R^2$ and a real convex polygon with vertices in the dyadic plane. Such polygons are described as subreducts (subalgebras of reducts) of the affine dyadic plane $D^2$, or equivalently as commutative, entropic and idempotent groupoids under the binary operation of arithmetic mean. The first part of the paper contained a new classification of dyadic triangles, considered as such groupoids, and a characterization of dyadic triangles with a pointed vertex. This second part investigates isomorphisms of dyadic triangles, and provides a full classification of their isomorphism types. |
| title | Geometry of dyadic polygons II: isomorphisms of dyadic triangles |
| topic | Combinatorics 08A05, 20N02, 52B11, 52A01 |
| url | https://arxiv.org/abs/2510.07244 |