Determinants of incidence and hessian matrices arising from the vector space lattice

Saeed Nasseh, Alexandra Seceleanu, Junzo Watanabe

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Let V = ∐ n i=0 V i be the lattice of sub- spaces of the n-dimensional vector space over the finite field F q , and let A be the graded Gorenstein algebra de- fined over Q which has V as a Q basis. Let F be the Macaulay dual generator for A. We explicitly compute the Hessian determinant |∂ 2 /∂X i ∂X j |, evaluated at the point X 1 = X 2 = ···= X N = 1, and relate it to the determinant of the incidence matrix between V 1 and V n-1 . Our explo- ration 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.

Original languageEnglish
Pages (from-to)131-154
Number of pages24
JournalJournal of Commutative Algebra
Volume11
Issue number1
DOIs
StatePublished - 2019

Keywords

  • Finite geometry
  • Gorenstein algebras
  • Hessian
  • Incidence matrix
  • Strong Lefschetz property
  • Vector space lattice

Fingerprint

Dive into the research topics of 'Determinants of incidence and hessian matrices arising from the vector space lattice'. Together they form a unique fingerprint.

Cite this