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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Abdallah et al. (2024) studied this question.
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