97 citations · 456 across the 44 of their papers we have counts for
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Three Ehrhart Quasi-polynomials
Velleda Baldoni, Nicole Berline, Jesús A. De Loera +2
Let be a semi-rational parametric polytope, where is a real multi-parameter. We study intermediate sums of polynomial functions on ,…
Intermediate Sums on Polyhedra II: Bidegree and Poisson Formula
Velleda Baldoni, Nicole Berline, Jesús A. De Loera +2
We continue our study of intermediate sums over polyhedra, interpolating between integrals and discrete sums, which were introduced by A. Barvinok [Computing the Ehrhart quasi-poly…
Poisson summation formula and Box splines
Michele Vergne
We generalize Dahmen-Micchelli deconvolution formula for Box splines with parameters. Our proof is based on identities for Poisson summation of rational functions with poles on hyp…
A relation between number of integral points, volumes of faces and degree of the discriminant of smooth lattice polytopes
Alicia Dickenstein, Benjamin Nill, Michèle Vergne
We present a formula for the degree of the discriminant of a smooth projective toric variety associated to a lattice polytope P, in terms of the number of integral points in the in…
A homotopy for a complex of free Lie algebras
Michele Vergne
Using the Guichardet construction, we compute the cohomology groups of a complex of free Lie algebras introduced by Alekseev and Torossian.
Intermediate Sums on Polyhedra: Computation and Real Ehrhart Theory
Velleda Baldoni, Nicole Berline, Matthias Köppe +1
We study intermediate sums, interpolating between integrals and discrete sums, which were introduced by A. Barvinok [Computing the Ehrhart quasi-polynomial of a rational simplex, M…