# Membership and elasticity in certain affine monoids

## TL;DR

This paper investigates the membership problem and elasticity of elements in specific affine monoids of dimension 2 with low embedding dimensions, providing insights into their algebraic structure.

## Contribution

It offers new criteria for membership and elasticity calculations in affine monoids of dimension 2 with embedding dimensions 2 and 3.

## Key findings

- Characterization of membership conditions in these monoids
- Formulas or methods for computing elasticity
- Enhanced understanding of the structure of low-dimensional affine monoids

## Abstract

For affine monoids of dimension 2 with embedding dimension 2 and 3, we study the problem of determining when a vector is an element of the monoid, and the problem of determining the elasticity of a monoid element.