Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long fully commutative elements in affine Coxeter groups   An element of a Coxeter group $W$ is called fully commutative if any two of
its reduced decompositions can be related by a series of transpositions of
adjacent commuting generators. In the preprint "Fully commutative elements in
finite and affine Coxeter groups" (arXiv:1402.2166), R. Biagioli and the
authors proved among other things that, for each irreducible affine Coxeter
group, the sequence counting fully commutative elements with respect to length
is ultimately periodic. In the present work, we study this sequence in its
periodic part for each of these groups, and in particular we determine the
minimal period. We also observe that in type $A$ affine we get an instance of
the cyclic sieving phenomenon.

18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph