## Illinois Journal of Mathematics

### The weak Lefschetz property, monomial ideals, and lozenges

#### Abstract

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

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

Dates
First available in Project Euclid: 19 December 2012

https://projecteuclid.org/euclid.ijm/1355927041

Digital Object Identifier
doi:10.1215/ijm/1355927041

Mathematical Reviews number (MathSciNet)
MR3006693

Zentralblatt MATH identifier
1262.13032

#### Citation

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. https://projecteuclid.org/euclid.ijm/1355927041

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