Lattice Paths, Lefschetz Properties, and Almkvist's Conjecture in Two Variables

2024/04/07 by Abdallah, Nancy, McDaniel, Chris
#05A10 #05B20 #11B83 #13E10 #13H10 #14F45 #15A15 #20F55 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.05098

Abstract

We study a certain two-parameter family of non-standard graded complete intersections A(m,n). In case n=2, we show that A(m,2) has the strong Lefschetz property and the complex Hodge-Riemann property if and only if m is even. This supports a strengthening of a conjecture of Almkvist on the unimodality of the Hilbert function of A(m,n).

Related

• Monomial Almost Complete Intersections and the Strong Lefschetz Property
• The strong Lefschetz property and simple extensions
• Enumerations of lozenge tilings, lattice paths, and perfect matchings and the weak Lefschetz property
• A new proof of Stanley's theorem on the strong Lefschetz property
• A tour of the Weak and Strong Lefschetz Properties