64 citations · 118 across the 13 of their papers we have counts for
14 papers
The Horn inequalities from a geometric point of view
Nicole Berline, Michèle Vergne, Michael Walter
We give an exposition of the Horn inequalities and their triple role characterizing tensor product invariants, eigenvalues of sums of Hermitian matrices, and intersections of Schub…
Local asymptotic Euler-Maclaurin expansion for Riemann sums over a semi-rational polyhedron
Nicole Berline, Michele Vergne
Consider the Riemann sum of a smooth compactly supported function h(x) on a polyhedron in R^d, sampled at the points of the lattice Z^d/t. We give an asymptotic expansion when t go…
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…
Coefficients of Sylvester's Denumerant
Velleda Baldoni, Nicole Berline, Jesús De Loera +3
For a given sequence of positive integers, we consider the combinatorial function that counts the nonnegative integer so…
Analytic continuation of a parametric polytope and wall-crossing
Nicole Berline, Michèle Vergne
We define a set theoretic "analytic continuation" of a polytope defined by inequalities. For the regular values of the parameter, our construction coincides with the parallel trans…