The number of polyiamonds is supermultiplicative
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866908449237893120 |
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| author | Bui, Vuong |
| author_facet | Bui, Vuong |
| contents | 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 $2.8578$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_10077 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The number of polyiamonds is supermultiplicative Bui, Vuong Combinatorics 05B50, 05A16 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 $2.8578$. |
| title | The number of polyiamonds is supermultiplicative |
| topic | Combinatorics 05B50, 05A16 |
| url | https://arxiv.org/abs/2304.10077 |