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arXiv · 2304.10077

The number of polyiamonds is supermultiplicative

Vuong Bui
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Abstract

While the number of polyominoes is known to be supermultiplicative by a simple concatenation argument, it is still unknown whether the same applies to polyiamonds. This article proves that if $\ell,m$ are not both $1$, then $T(\ell+m)\ge T(\ell)T(m)$, for which one can say that the number of polyiamonds $T(n)$ is supermultiplicative. The method is, however, by concatenating, merging and adding cells at the same time. A corollary is an increment of the best known lower bound on the growth constant from $2.8423$ to $2.8578$.

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Vuong Bui. 2023-11-17. The number of polyiamonds is supermultiplicative. https://doi.org/10.37236/12028

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