Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the growth of deviations   The deviations of a graded algebra are a sequence of integers that determine
the Poincare series of its residue field and arise as the number of generators
of certain DG algebras. In a sense, deviations measure how far a ring is from
being a complete intersection. In this paper we study extremal deviations among
those of algebras with a fixed Hilbert series. In this setting, we prove that,
like the Betti numbers, deviations do not decrease when passing to an initial
ideal and are maximized by the Lex-segment ideal. We also prove that deviations
grow exponentially for Golod rings and for certain quadratic monomial algebras.

8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph