3,701 research outputs found
Determinants of incidence and Hessian matrices arising from the vector space lattice
Let be the lattice of subspaces
of the -dimensional vector space over the finite field and
let be the graded Gorenstein algebra defined over
which has as a basis. Let be the Macaulay dual
generator for . We compute explicitly the Hessian determinant
evaluated at the point and relate it to the determinant of the incidence
matrix between and . Our exploration is
motivated by the fact that both of these matrices arise naturally in the study
of the Sperner property of the lattice and the Lefschetz property for the
graded Artinian Gorenstein algebra associated to it
Lattice Diagram polynomials in one set of variables
The space spanned by all partial derivatives of the lattice
polynomial is investigated in math.CO/9809126 and many
conjectures are given. Here, we prove all these conjectures for the -free
component of . In particular, we give an explicit
bases for which allow us to prove directly the central {\sl
four term recurrence} for these spaces.Comment: 15 page
Hunting for the New Symmetries in Calabi-Yau Jungles
It was proposed that the Calabi-Yau geometry can be intrinsically connected
with some new symmetries, some new algebras. In order to do this it has been
analyzed the graphs constructed from K3-fibre CY_d (d \geq 3) reflexive
polyhedra. The graphs can be naturally get in the frames of Universal
Calabi-Yau algebra (UCYA) and may be decode by universal way with changing of
some restrictions on the generalized Cartan matrices associated with the Dynkin
diagrams that characterize affine Kac-Moody algebras. We propose that these new
Berger graphs can be directly connected with the generalizations of Lie and
Kac-Moody algebras.Comment: 29 pages, 15 figure
Chern classes of Schubert cells and varieties
We give explicit formulas for the Chern-Schwartz-MacPherson classes of all
Schubert varieties in the Grassmannian of -planes in a vector space, and
conjecture that these classes are effective. We prove this is the case for
(very) small values of .Comment: 31 pages, several figure
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