On the index of powers of edge ideals

ABSTRACT

The index of a graded ideal measures the number of linear steps in the graded minimal free resolution of the ideal. In this paper, we study the index of powers and squarefree powers of edge ideals. Our results indicate that the index as a function of the power of an edge ideal I is strictly increasing if I is linearly presented. Examples show that this needs not to be the case for monomial ideals generated in degree greater than two.

KEYWORDS:

• Edge ideals
• index
• powers of ideals
• resolutions

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 13D02, 13C13
• Secondary 05E40

Acknowledgements

The paper was written while the first author was visiting the Department of Mathematics of University Duisburg-Essen. She wants to express her thanks for its hospitality.