# The divisor class group of a discrete polymatroid

## TL;DR

This paper introduces toric rings of multicomplexes, focusing on computing their divisor class groups and canonical modules, especially for discrete polymatroids, providing new insights into their algebraic structure.

## Contribution

It develops methods to compute divisor class groups and canonical modules of toric rings associated with multicomplexes, with detailed analysis for discrete polymatroids.

## Key findings

- Computed divisor class groups for normal toric rings of multicomplexes.
- Analyzed the structure of toric rings for various classes of discrete polymatroids.
- Provided explicit descriptions of canonical modules in these cases.

## Abstract

In this paper we introduce toric rings of multicomplexes. We show how to compute the divisor class group and the class of the canonical module when the toric ring is normal. In the special case that the multicomplex is a discrete polymatroid, its toric ring is studied deeply for several classes of polymatroids.