Arkiv för Matematik

Volume 55 (2017)

Number 1

The behavior of depth functions of cover ideals of unimodular hypergraphs

Pages: 89 – 104

DOI: https://dx.doi.org/10.4310/ARKIV.2017.v55.n1.a4

Authors

Nguyen Thu Hang (College of Sciences, Thai Nguyen University, Thai Nguyen, Vietnam)

Tran Nam Trung (Institute of Mathematics, VAST, Hanoi, Vietnam)

Abstract

We prove that the cover ideals of all unimodular hypergraphs have the non-increasing depth function property. Furthermore, we show that the index of depth stability of these ideals is bounded by the number of variables.

Keywords

depth function, cover ideals, powers of ideals

2010 Mathematics Subject Classification

13A15, 13C13

Full Text (PDF format)

This work is partially supported by NAFOSTED (Vietnam) under the grant number 101.04-2015.02. The first author is also partially supported by Thai Nguyen university of Science under the grant number ÐH2016-TN06-03.

Received 14 January 2016

Accepted 8 September 2016

Published 26 September 2017