Acta Mathematica Vietnamica

, Volume 44, Issue 1, pp 117–139 | Cite as

Membership Criteria and Containments of Powers of Monomial Ideals

  • Huy Tài Hà
  • Ngo Viet TrungEmail author


We present a close relationship between matching number, covering numbers and their fractional versions in combinatorial optimization and ordinary powers, integral closures of powers, and symbolic powers of monomial ideals. This relationship leads to several new results and problems on the containments between these powers.


Monomial ideal Ordinary power Symbolic power Integral closure of a power Hypergraph Matching Covering Gap estimate Edge ideal Containments between powers of ideals Generating degree 

Mathematics Subject Classification (2010)

13C05 05C65 90C27 



This paper started during a research stay of the authors at Vietnam Institute for Advanced Study in Mathematics. The authors would like to thank the institute for its support and hospitality.

Funding Information

The first author is partially supported by Simons Foundation (grant # 279786) and Louisiana Board of Regents (grant # LEQSF(2017-19)-ENH-TR-25). The second author is supported by Vietnam National Foundation for Science and Technology Development (grant # 101.04-2017.19).


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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of MathematicsTulane UniversityNew OrleansUSA
  2. 2.International Centre for Research and Postgraduate Training, Institute of MathematicsVietnam Academy of Science and TechnologyHanoiVietnam

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