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arXiv · 2404.05098

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

Nancy Abdallah·Chris McDaniel
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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 $A(m,n)$.

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Nancy Abdallah, Chris McDaniel. 2024-04-07. Lattice Paths, Lefschetz Properties, and Almkvist's Conjecture in Two Variables. https://arxiv.org/abs/2404.05098

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