Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting Collisions in an $N$-Billiard System Using Angles Between
  Collision Subspaces   The principal angles between binary collision subspaces in an $N$-billiard
system in $d$-dimensional Euclidean space are computed. These angles are
computed for equal masses and arbitrary masses. We then provide a bound on the
number of collisions in the planar 3-billiard system problem. Comparison of
this result with known billiard collision bounds in lower dimensions is
discussed.

33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
8
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: chao-dyn
14
The categories of this paper are: math-ph