Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Betti numbers of some semigroup rings   For any numerical semigroup $S$, there are infinitely many numerical
symmetric semigroups $T$ such that $S=\frac{T}{2}$ is their half. We are
studying the Betti numbers of the numerical semigroup ring $K[T]$ when $S$ is a
3-generated numerical semigroup or telescopic. We also consider 4-generated
symmetric semigroups and the so called 4-irreducible numerical semigroups.

35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc