Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the set of elasticities in numerical monoids   In an atomic, cancellative, commutative monoid $S$, the elasticity of an
element provides a coarse measure of its non-unique factorizations by comparing
the largest and smallest values in its set of factorization lengths (called its
length set). In this paper, we show that the set of length sets $\mathcal L(S)$
for any arithmetical numerical monoid $S$ can be completely recovered from its
set of elasticities $R(S)$; therefore, $R(S)$ is as strong a factorization
invariant as $\mathcal L(S)$ in this setting. For general numerical monoids, we
describe the set of elasticities as a specific collection of monotone
increasing sequences with a common limit point of $\max R(S)$.

21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga