Equilateral convex triangulations of $\mathbb R P^2$ with three conical points of equal defect
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866908625471012864 |
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| author | Chernavskikh, Mikhail Erdnigor, Altan Kalinin, Nikita Zakharov, Alexandr |
| author_facet | Chernavskikh, Mikhail Erdnigor, Altan Kalinin, Nikita Zakharov, Alexandr |
| contents | Consider triangulations of $\mathbb R P^2$ whose all vertices have valency six except three vertices of valency $4$. In this chapter we prove that the number $f(n)$ of such triangulations with no more than $n$ triangles grows as $C\cdot n^2+ O(n^{3/2})$ where $C = \frac{1}{20} \sqrt{3} \cdot L( \fracπ{3} ) ζ^{-1}(4) ζ(Eis, 2) \approx 0.2087432125056015...$, where $L$ is the Lobachevsky function and $ζ(Eis,2) =\sum\limits_{(a,b)\in\mathbb Z^2\setminus 0}{\frac{1}{|a+bω^2|^4}}$, and $ω^6=1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_04680 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Equilateral convex triangulations of $\mathbb R P^2$ with three conical points of equal defect Chernavskikh, Mikhail Erdnigor, Altan Kalinin, Nikita Zakharov, Alexandr Combinatorics Differential Geometry Metric Geometry Number Theory 51M09, 57N45, 11P21, 11M36, 11E45 Consider triangulations of $\mathbb R P^2$ whose all vertices have valency six except three vertices of valency $4$. In this chapter we prove that the number $f(n)$ of such triangulations with no more than $n$ triangles grows as $C\cdot n^2+ O(n^{3/2})$ where $C = \frac{1}{20} \sqrt{3} \cdot L( \fracπ{3} ) ζ^{-1}(4) ζ(Eis, 2) \approx 0.2087432125056015...$, where $L$ is the Lobachevsky function and $ζ(Eis,2) =\sum\limits_{(a,b)\in\mathbb Z^2\setminus 0}{\frac{1}{|a+bω^2|^4}}$, and $ω^6=1$. |
| title | Equilateral convex triangulations of $\mathbb R P^2$ with three conical points of equal defect |
| topic | Combinatorics Differential Geometry Metric Geometry Number Theory 51M09, 57N45, 11P21, 11M36, 11E45 |
| url | https://arxiv.org/abs/2111.04680 |