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 2 295-317

Ämneskategorier (SSIF 2025)

Algebra och logik

DOI

10.5802/alco.414

Mer information

Senast uppdaterat

2025-05-23