Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Binomial ideals of domino tilings   In this paper, we consider the set of all domino tilings of a cubiculated
region. The primary question we explore is: How can we move from one tiling to
another? Tiling spaces can be viewed as spaces of subgraphs of a fixed graph
with a fixed degree sequence. Moves to connect such spaces have been explored
in algebraic statistics. Thus, we approach this question from an applied
algebra viewpoint, making new connections between domino tilings, algebraic
statistics, and toric algebra. Using results from toric ideals of graphs, we
are able to describe moves that connect the tiling space of a given cubiculated
region of any dimension. This is done by studying binomials that arise from two
distinct domino tilings of the same region. Additionally, we introduce tiling
ideals and flip ideals and use these ideals to restate what it means for a
tiling space to be flip connected. Finally, we show that if $R$ is a
$2$-dimensional simply connected cubiculated region, any binomial arising from
two distinct tilings of $R$ can be written in terms of quadratic binomials. As
a corollary to our main result, we obtain an alternative proof to the fact that
the set of domino tilings of a $2$-dimensional simply connected region is
connected by flips.

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The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn