Abstract
We give explicit formulas for the determinants of the incidence and Hessian matrices arising from the interaction between the rank 1 and rank n−1 level sets of the subspace lattice of an n-dimensional finite vector space. Our exploration is motivated by the fact that both of these matrices arise naturally in the study of the combinatorial and algebraic Lefschetz properties for the vector space lattice and the graded Artinian Gorenstein algebra associated to it, respectively.
| Original language | American English |
|---|---|
| Journal | Journal of Commutative Algebra |
| State | Published - Jan 1 2014 |
Disciplines
- Education
- Mathematics
Keywords
- Algebraic properties
- Artinian Gorenstein algebra
- Combinatorial properties
- Finite vector space
- Hessian matrices
- Incidence
- Lefschetz properties
- Subspace lattice
- Vector space lattice