Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On polynomials with given Hilbert function and applications   Using Macaulay's correspondence we study the family of Artinian Gorenstein
local algebras with fixed symmetric Hilbert function decomposition. As an
application we give a new lower bound for cactus varieties of the third
Veronese embedding. We discuss the case of cubic surfaces, where interesting
phenomena occur.

30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph