A Formal Analogue of Euler's Formula for Infinite Planar Regular Graphs
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918249732505600 |
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| author | Jędrzejewicz, Piotr Marciniak, Mikołaj |
| author_facet | Jędrzejewicz, Piotr Marciniak, Mikołaj |
| contents | We present a formal version of the numbers of vertices, edges, and faces for infinite planar regular triangular meshes of degree r>6. These numbers are defined via Euler summation of sequences obtained from iterated expansions of a convex combinatorial disk. We prove that these formal quantities satisfy the classical Euler formula, providing a combinatorial analogue of Euler's formula for infinite planar graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14030 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Formal Analogue of Euler's Formula for Infinite Planar Regular Graphs Jędrzejewicz, Piotr Marciniak, Mikołaj Combinatorics We present a formal version of the numbers of vertices, edges, and faces for infinite planar regular triangular meshes of degree r>6. These numbers are defined via Euler summation of sequences obtained from iterated expansions of a convex combinatorial disk. We prove that these formal quantities satisfy the classical Euler formula, providing a combinatorial analogue of Euler's formula for infinite planar graphs. |
| title | A Formal Analogue of Euler's Formula for Infinite Planar Regular Graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2512.14030 |