Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Real phase structures on matroid fans and matroid orientations   We introduce the notion of real phase structure on rational polyhedral fans
in Euclidean space. Such a structure consists of an assignment of affine spaces
over $\mathbb{Z}/2\mathbb{Z}$ to each top dimensional face of the fan subject
to two conditions. Given an oriented matroid we can construct a real phase
structure on the fan of the underlying matroid. Conversely, we show that from a
real phase structure on a matroid fan we can produce an orientation of the
underlying matroid. Thus real phase structures are cryptomorphic to matroid
orientations. The topes of the orientated matroid are recovered immediately
from the real phase structure. We also provide a direct way to recover the
signed circuits of the oriented matroid from the real phase structure.

30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
15
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: alg-geom
10
The categories of this paper are: q-bio
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The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg