Gespeichert in:
| 1. Verfasser: | |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2510.06806 |
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Inhaltsangabe:
- We provide a short and elementary proof that the growth constant of polyiamonds is at most $1+2z+3z^2$ for the unique real root $z$ of the equation $2z^3+z^2-1=0$. This coincidentally suffices to recover the best known upper bound $3.6108$. Unlike the previous proof of this bound, which relied on computer-assisted technical arguments and the counts of polyiamonds with up to 75 triangles, our method is based on a straightforward recurrence that can be verified by hand with minimal effort.