Some interpretations for algebraic invariants of edge ideals of hypergraphs via combinatorial invariants

Abstract

The present work is concerned with characterizing some algebraic invariants of edge ideals of hypergraphs. To this aim, first, we introduce some kinds of combinatorial invariants similar to matching numbers for hypergraphs. Then we compare them to each other and to previously existing ones. These invariants are used for characterizing or bounding some algebraic invariants of edge ideals of hypergraphs such as graded Betti numbers, projective dimension and Castelnouvo–Mumford regularity.

Communicated by Jason P. Bell

Keywords:

• Graded Betti numbers
• projective dimension
• regularity
• triangulated hypergraph

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 13F55
• 13D02
• 05C90
• Secondary 05E99

Acknowledgment

The authors would like to thank the anonymous reviewer whose comments and remarks improved the presentation of the paper.