Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lozenge tilings of hexagons with holes on three crossing lines   The enumeration of lozenge tilings of hexagons with holes has received much
attention during the last three decades. One notable feature is that a lot of
the recent development involved Kuo's graphical condensation. Motivated by
Ciucu, Lai and Rohatgi's work on tilings of hexagons with a removed triad of
bowties, in this paper, we show that the ratio of numbers of lozenge tilings of
two more general regions is expressed as a simple product formula. Our proof
does not involve the graphical condensation method. The proof is short and
direct. We also provide a corresponding formula for cyclically symmetric
lozenge tilings. Several previous results can be easily deduced from our
generalization.

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The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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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: supr-con
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex