Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Number of cycles in the graph of 312-avoiding permutations   The graph of overlapping permutations is defined in a way analogous to the De
Bruijn graph on strings of symbols. That is, for every permutation $\pi =
\pi_{1} \pi_{2} ... \pi_{n+1}$ there is a directed edge from the
standardization of $\pi_{1} \pi_{2} ... \pi_{n}$ to the standardization of
$\pi_{2} \pi_{3} ... \pi_{n+1}$. We give a formula for the number of cycles of
length $d$ in the subgraph of overlapping 312-avoiding permutations. Using this
we also give a refinement of the enumeration of 312-avoiding affine
permutations and point out some open problems on this graph, which so far has
been little studied.

28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat