Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Hilbert function of the tangent cone of a monomial curve   In this paper we study the Hilbert function of $\gr_{\mathfrak{m}}(R)$, when
$R$ is a numerical semigroup ring or, equivalently, the coordinate ring of a
monomial curve. In particular, we prove a sufficient condition for a numerical
semigroup ring in order get a non-decreasing Hilbert function, without making
any assumption on its embedding dimension; moreover, we show how this new
condition allows to improve known results about this problem. To this aim we
use certain invariants of the semigroup, with particular regard to its
\Apery-set.

3
The categories of this paper are: physics
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat