Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Factorization invariants of Puiseux monoids generated by geometric
  sequences   We study some of the factorization invariants of the class of Puiseux monoids
generated by geometric sequences, and we compare and contrast them with the
known results for numerical monoids generated by arithmetic sequences. The
class we study consists of all atomic monoids of the form $S_r := \langle r^n
\mid n \in \mathbb{N}_0 \rangle,$ where $r$ is a positive rational. As the
atomic monoids $S_r$ are nicely generated, we are able to give detailed
descriptions of many of their factorization invariants. One distinguishing
characteristic of $S_r$ is that all its sets of lengths are arithmetic
sequences of the same distance, namely $|a-b|$, where $a,b \in \mathbb{N}$ are
such that $r = a/b$ and $\text{gcd}(a,b) = 1$. We prove this, and then use it
to study the elasticity and tameness of $S_r$.

23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph