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Spring 2011 The weak Lefschetz property, monomial ideals, and lozenges
David Cook II, Uwe Nagel
Illinois J. Math. 55(1): 377-395 (Spring 2011). DOI: 10.1215/ijm/1355927041


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.


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David Cook II. Uwe Nagel. "The weak Lefschetz property, monomial ideals, and lozenges." Illinois J. Math. 55 (1) 377 - 395, Spring 2011.


Published: Spring 2011
First available in Project Euclid: 19 December 2012

zbMATH: 1262.13032
MathSciNet: MR3006693
Digital Object Identifier: 10.1215/ijm/1355927041

Primary: 13E10
Secondary: 13C40

Rights: Copyright © 2011 University of Illinois at Urbana-Champaign


Vol.55 • No. 1 • Spring 2011
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