Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fibonacci numbers and positive braids   The paper contains enumerative combinatorics for positive braids, square free
braids, and simple braids, emphasizing connections with classical Fibonacci
sequence. The simple subgraph of the Cayley graph of the braid group is
analyzed in the final part.

3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph