Lattice Paths, Lefschetz Properties, and Almkvist’s Conjecture in Two Variables
Artikel i vetenskaplig tidskrift, 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
Författare
Nancy Abdallah
Högskolan i Borås
Göteborgs universitet
Chalmers, Matematiska vetenskaper, Algebra och geometri
Chris McDaniel
Endicott College
Algebraic Combinatorics
25895486 (eISSN)
Vol. 8 2 295-317Ämneskategorier (SSIF 2025)
Algebra och logik
DOI
10.5802/alco.414