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Abstract
In this paper we study the Freiman inequality for the least number of generators of the square of an equigenerated monomial ideal. Such an ideal is called a Freiman ideal if equality holds in the Freiman inequality. We classify all Freiman ideals of maximal height, the Freiman ideals of certain classes of principal Borel ideals, the Hibi ideals which are Freiman, and classes of Veronese type ideals which are Freiman.
2010 Mathematics Subject Classification:
Acknowledgements
We would like to thank the referee for a careful reading and pertinent comments. The paper was also written while the second author Guangjun Zhu was visiting the Department of Mathematics of University Duisburg-Essen. She want to express her thanks for the hospitality.
Additional information
Funding
This paper is supported by the National Natural Science Foundation of China [11271275] and by the Foundation of the Priority Academic Program Development of Jiangsu Higher Education Institutions.