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- W2962976157 abstract "Let $mathcal {V}=bigsqcup _{i=0}^nmathcal {V}_i$ be the lattice of subspaces of the $n$-dimensional vector space over the finite field $mathbb{F} _q$, and let $mathcal {A}$ be the graded Gorenstein algebra defined over $mathbb{Q} $ which has $mathcal {V}$ as a $mathbb{Q} $ basis. Let $F$ be the Macaulay dual generator for $mathcal {A}$. We explicitly compute the Hessian determinant $|{partial ^2F}/{partial X_i partial X_j}|$, evaluated at the point $X_1 = X_2 = cdots = X_N=1$, and relate it to the determinant of the incidence matrix between $mathcal {V}_1$ and $mathcal {V}_{n-1}$. Our exploration is motivated by the fact that both of these matrices naturally arise in the study of the Sperner property of the lattice and the Lefschetz property for the graded Artinian Gorenstein algebra associated to it." @default.
- W2962976157 created "2019-07-30" @default.
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- W2962976157 date "2019-02-01" @default.
- W2962976157 modified "2023-09-24" @default.
- W2962976157 title "Determinants of incidence and Hessian matrices arising from the vector space lattice" @default.
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- W2962976157 doi "https://doi.org/10.1216/jca-2019-11-1-131" @default.
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