Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tilings of convex sets by mutually incongruent equilateral triangles
  contain arbitrarily small tiles   We show that every tiling of a convex set in the Euclidean plane
$\mathbb{R}^2$ by equilateral triangles of mutually different sizes contains
arbitrarily small tiles. The proof is purely elementary up to the discussion of
one family of tilings of the full plane $\mathbb{R}^2$, which is based on a
surprising connection to a random walk on a directed graph.

15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph