Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Graded Betti numbers of balanced simplicial complexes
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex