Physical Sciences and Mathematics Commons^™

Determinants Of Incidence And Hessian Matrices Arising From The Vector Space Lattice, Saeed Nasseh, Alexandra Seceleanu, Junzo Watanabe

Department of Mathematical Sciences Faculty Publications

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.