Asymptotic lower bounds for modular and semimodular lattices
Jukka Kohonen · arXiv (Cornell University) · 2018
Using vertical sums of small lattices, we prove that the numbers of nonisomorphic modular and semimodular lattices of $n$ elements grow at least as $\Omega(2.2630^n)$ and $\Omega(2.6421^n)$, respectively. For vertically indecomposable modular and semimodular lattices, we prove the lower bounds $\Omega(2.058^n)$ and $\Omega(2.5249^n)$ by using the vertical 2-sum, which combines lattices at two common elements.