Geodesic
The number of polyiamonds is supermultiplicative
Vuong Bui1
1Institut für Informatik, Freie Universität Berlin
The electronic journal of combinatorics, Tome 30 (2023) no. 4
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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 $2.8578$.
DOI : 10.37236/12028
Classification : 05B50, 05A16, 05A15
Mots-clés : polyominoes, equivalent lattice animals

Vuong Bui  1

1 Institut für Informatik, Freie Universität Berlin 
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Vuong Bui. The number of polyiamonds is supermultiplicative. The electronic journal of combinatorics, Tome 30 (2023) no. 4. doi: 10.37236/12028

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