Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Enumeration of quarter-turn symmetric alternating-sign matrices of odd
  order   It was shown by Kuperberg that the partition function of the square-ice model
related to the quarter-turn symmetric alternating-sign matrices of even order
is the product of two similar factors. We propose a square-ice model whose
states are in bijection with the quarter-turn symmetric alternating-sign
matrices of odd order, and show that the partition function of this model can
be also written in a similar way. This allows to prove, in particular, the
conjectures by Robbins related to the enumeration of the quarter-turn symmetric
alternating-sign matrices.

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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th