Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: The possible extremal Betti numbers of a homogeneous ideal
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph