# Monomial multiplicities in explicit form

## TL;DR

This paper provides explicit formulas for the multiplicities of various classes of monomial ideals, including codimension 1 ideals, almost complete intersections, and a new extended class, with visual interpretations.

## Contribution

It introduces new formulas for multiplicities of specific monomial ideals and defines a new class extending monomial complete intersections.

## Key findings

- Formulas for multiplicities of codimension 1 monomial ideals
- Formulas for multiplicities of almost complete intersections
- Introduction of a new class of ideals with multiplicity formula

## Abstract

In this article we give explicit descriptions of the multiplicities of some classes of monomial ideals. For instance, we give a formula for the multiplicities of all codimension 1 monomial ideals, and another formula for the multiplicities of almost complete intersections. We also introduce a new class of ideals that extends the family of monomial complete intersections, and give a formula for their multiplicity, as well as a visual interpretation of this invariant.