Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The depth of powers of an ideal   We study the limit and initial behavior of the numerical function
$f(k)=\depth S/I^k$. General properties of this function together with concrete
examples arising from combinatorics are discussed.

8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th