# Unmixedness and arithmetic properties of matroidal ideals

## TL;DR

This paper investigates the algebraic and combinatorial properties of matroidal ideals, establishing their unmixedness and proving that their arithmetical rank equals n minus the degree plus one, confirming a conjecture by Chiang-Hsieh.

## Contribution

It provides a proof that the arithmetical rank of matroidal ideals equals n minus the degree plus one, confirming a conjecture and exploring their unmixedness properties.

## Key findings

- Proves that the arithmetical rank of matroidal ideals is n - d + 1.
- Shows that matroidal ideals are unmixed under certain conditions.
- Confirms a conjecture by Chiang-Hsieh regarding arithmetical rank.

## Abstract

Let $R=k[x_1,...,x_n]$ be the polynomial ring in $n$ variables over a field $k$ and $I$ be a matroidal ideal of degree $d$. In this paper, we study the unmixedness properties and the arithmetical rank of $I$. Moreover, we show that $ara(I)=n-d+1$. This answer to the conjecture that made by H. J. Chiang-Hsieh \cite[Conjecture]{C}.