Incidences, tilings, and fields
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908917259304960 |
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| author | Pylyavskyy, P. Skopenkov, M. |
| author_facet | Pylyavskyy, P. Skopenkov, M. |
| contents | The master theorem, introduced by Richter-Gebert and generalized by Fomin and the first author, provides a method for proving incidence theorems of projective geometry using triangular tilings of surfaces. We investigate which incidence theorems over C and R can or cannot be proved via the master theorem. For this, we formalize the notion of a tiling proof. We introduce a hierarchy of classes of theorems based on the underlying topological spaces. A key tool is considering the same theorems over finite fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02229 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Incidences, tilings, and fields Pylyavskyy, P. Skopenkov, M. Combinatorics Geometric Topology Metric Geometry 51A20, 05E14, 14N20, 51M15, 57Q05, 12E20 The master theorem, introduced by Richter-Gebert and generalized by Fomin and the first author, provides a method for proving incidence theorems of projective geometry using triangular tilings of surfaces. We investigate which incidence theorems over C and R can or cannot be proved via the master theorem. For this, we formalize the notion of a tiling proof. We introduce a hierarchy of classes of theorems based on the underlying topological spaces. A key tool is considering the same theorems over finite fields. |
| title | Incidences, tilings, and fields |
| topic | Combinatorics Geometric Topology Metric Geometry 51A20, 05E14, 14N20, 51M15, 57Q05, 12E20 |
| url | https://arxiv.org/abs/2505.02229 |