# Sequentially Cohen-Macaulay matroidal ideals

## TL;DR

This paper investigates the class of sequentially Cohen-Macaulay matroidal ideals in polynomial rings, providing classifications for degree 2 and some cases for degree 3 or higher.

## Contribution

It offers a complete classification of degree 2 sequentially Cohen-Macaulay matroidal ideals and partial classifications for higher degrees in specific cases.

## Key findings

- All degree 2 sequentially Cohen-Macaulay matroidal ideals are classified.
- Partial classification results for degree d ≥ 3 in certain cases.
- Provides structural insights into matroidal ideals with Cohen-Macaulay properties.

## Abstract

Let $R=K[x_1,...,x_n]$ be the polynomial ring in $n$ variables over a field $K$ and let $J$ be a matroidal ideal of degree $d$ in $R$. In this paper, we study the class of sequentially Cohen-Macaulay matroidal ideals. In particular, all sequentially Cohen-Macaulay matroidal ideals of degree $2$ are classified. Furthermore, we give a classification of sequentially Cohen-Macaulay matroidal ideals of degree $d\geq 3$ in some special cases.