Lattice Paths, Lefschetz Properties, and Almkvist’s Conjecture in Two Variables
Journal article, 2025
We study a certain two-parameter family of non-standard graded complete intersection algebras A(m, n). In case n = 2, we show that if m is even then A(m, 2) has the strong Lefschetz property and satisfies the complex Hodge–Riemann relations, while if m is odd then A(m, 2) satisfies these properties only up to a certain degree. This supports a strengthening of a conjecture of Almkvist on the unimodality of the Hilbert function of A(m, n).
strong Lefschetz property
Hodge–Riemann property
pseudo-reflection group
higher Hessian
NE lattice paths
binomial determinants
Author
Nancy Abdallah
University of Borås
University of Gothenburg
Chalmers, Mathematical Sciences, Algebra and geometry
Chris McDaniel
Endicott College
Algebraic Combinatorics
25895486 (eISSN)
Vol. 8 2 295-317Subject Categories (SSIF 2025)
Algebra and Logic
DOI
10.5802/alco.414