Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cyclopermutohedron: geometry and topology   The face poset of the permutohedron realizes the combinatorics of linearly
ordered partitions of the set $[n]=\{1,...,n\}$. Similarly, the
cyclopermutohedron is a virtual polytope that realizes the combinatorics of
cyclically ordered partitions of the set $[n+1]$. The cyclopermutohedron was
introduced by the third author by motivations coming from configuration spaces
of polygonal linkages. In the paper we prove two facts: (1) the volume of the
cyclopermutohedron equals zero, and (2) the homology groups $H_k$ for
$k=0,...,n-2$ of the face poset of the cyclopermutohedron are non-zero free
abelian groups. We also present a short formula for their ranks.

15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph