Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exponential lower bounds of lattice counts by vertical sum and 2-sum   We consider the problem of finding lower bounds on the number of unlabeled
$n$-element lattices in some lattice family. We show that if the family is
closed under vertical sum, exponential lower bounds can be obtained from
vertical sums of small lattices whose numbers are known. We demonstrate this
approach by establishing that the number of modular lattices is at least
$2.2726^n$ for $n$ large enough.
  We also present an analogous method for finding lower bounds on the number of
vertically indecomposable lattices in some family. For this purpose we define a
new kind of sum, the vertical 2-sum, which combines lattices at two common
elements. As an application we prove that the numbers of vertically
indecomposable modular and semimodular lattices are at least $2.1562^n$ and
$2.6797^n$ for $n$ large enough.

19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol