Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pairs of Full-Rank Lattices With Parallelepiped-Shaped Common
  Fundamental Domains   We provide a complete characterization of pairs of full-rank lattices in
$\mathbb{R}^{d}$ which admit common connected fundamental domains of the type
$N\left[ 0,1\right) ^{d}$ where $N$ is an invertible matrix of order $d.$ Using
our characterization, we construct several pairs of lattices of the type
$\left( M\mathbb{Z}^{d},\mathbb{Z}^{d}\right) $ which admit a common
fundamental domain of the type $N\left[ 0,1\right) ^{d}.$ Moreover, we show
that for $d=2,$ there exists an uncountable family of pairs of lattices of the
same volume which do not admit a common connected fundamental domain of the
type $N\left[ 0,1\right) ^{2}.$

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The categories of this paper are: econ
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat