Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Graded Betti numbers of powers of ideals
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex