Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Squarability of rectangle arrangements   We study when an arrangement of axis-aligned rectangles can be transformed
into an arrangement of axis-aligned squares in $\mathbb{R}^2$ while preserving
its structure. We found a counterexample to the conjecture of J. Klawitter, M.
N\"ollenburg and T. Ueckerdt whether all arrangements without crossing and
side-piercing can be squared. Our counterexample also works in a more general
case when we only need to preserve the intersection graph and we forbid
side-piercing between squares. We also show counterexamples for transforming
box arrangements into combinatorially equivalent hypercube arrangements.
Finally, we introduce a linear program deciding whether an arrangement of
rectangles can be squared in a more restrictive version where the order of all
sides is preserved.

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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: math
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio