Sequentially cohen-macaulay matroidal ideals

Abstract

Let R = K[x1,...,xn] be the polynomial ring in n variables over a field K and let I be a matroidal ideal of degree d in R. Our main focus is determining when matroidal ideals are sequentially Cohen- Macaulay. 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 ? 3 in some special cases.