# The existence of non-thin subalgebras of $K[x]/x^n$ and related numerical monoids

## TL;DR

This paper investigates the minimal dimension of truncated polynomial algebras over any field that contain non-thin subalgebras, providing examples and counting them in low dimensions.

## Contribution

It identifies the minimal dimension for non-thin subalgebras in truncated polynomial algebras and explores their examples and enumeration.

## Key findings

- Minimal dimension for non-thin subalgebras determined
- Examples of non-thin subalgebras provided
- Counting of subalgebras in low dimensions conducted

## Abstract

We find the minimal dimension for a truncated polynomial algebra over an arbitrary field for which there exists a "non-thin" subalgebra. Moreover, we discuss examples of subalgebras, and count them in low dimensions.