Illinois Journal of Mathematics

The weak Lefschetz property, monomial ideals, and lozenges

David Cook II and Uwe Nagel

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We study the weak Lefschetz property and the Hilbert function of level Artinian monomial almost complete intersections in three variables. Several such families are shown to have the weak Lefschetz property if the characteristic of the base field is zero or greater than the maximal degree of any minimal generator of the ideal. Two of the families have an interesting relation to tilings of hexagons by lozenges. This lends further evidence to a conjecture by Migliore, Miró-Roig, and the second author. Finally, using our results about the weak Lefschetz property, we show that the Hilbert function of each level Artinian monomial almost complete intersection in three variables is peaked strictly unimodal.

Article information

Illinois J. Math., Volume 55, Number 1 (2011), 377-395.

First available in Project Euclid: 19 December 2012

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Zentralblatt MATH identifier

Primary: 13E10: Artinian rings and modules, finite-dimensional algebras
Secondary: 13C40: Linkage, complete intersections and determinantal ideals [See also 14M06, 14M10, 14M12]


Cook II, David; Nagel, Uwe. The weak Lefschetz property, monomial ideals, and lozenges. Illinois J. Math. 55 (2011), no. 1, 377--395. doi:10.1215/ijm/1355927041.

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