LATTICE POINTS OF DILATIONS OF THE STANDARD 2-SIMPLEX AND THE GRASSMANNIAN Gr(2,n)

ON THE LATTICE POINTS OF DILATIONS

Abstract

The connection between the combinatorics of the lattice points of the dilation r∆2 of the standard 2-simplex ∆2 and the cohomology ring of the Grasmmannian Gr(2, r+2) is explored. Specifically, two important refinements of the Ehrhart polynomial
are realized from this connection. One of the refinements interprets the Poincar´epolynomial P(Gr(2, r + 2), z) as the number of lattice points on each of the slicing lines of r∆2 with respect to a fixed weight.