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.
From: Jan Florek [view email]
[v1]
Thu, 17 Apr 2025 20:03:00 UTC (21 KB)
[v2]
Mon, 21 Apr 2025 16:04:54 UTC (21 KB)
[v3]
Mon, 31 Aug 2026 07:21:22 UTC (17 KB)
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