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arXiv · 2504.13316

The enumeration of plane (3,6)-triangulations and the form of odd perfect numbers

Jan Florek
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Abstract

Let $\mathcal{P}$ be the family of all $3$-connected plane triangulations with vertices of degree $3$ or $6$. The number $d(n)$ of non-isomorphic triangulations belonging to $\mathcal{P}$ of degree $2n+2$ are enumerated, for $n \geqslant 1$. From the formula for $d(n)$ (where $n$ is odd and $n > 1$), we obtain a strengthening of Euler's theorem regarding the form of odd perfect number.

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Jan Florek. 2026-08-31. The enumeration of plane (3,6)-triangulations and the form of odd perfect numbers. https://arxiv.org/abs/2504.13316

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