6 citations · 11 across the 7 of their papers we have counts for
7 papers
Explicit computations of Fourier transforms of polyhedral cones
Quang-Nhat Le
The Fourier transforms of polyhedral cones can be used, via Brion's theorem, to compute various geometric quantities of polytopes, such as volumes, moments, and lattice-point count…
New irrational polygons with Ehrhart-theoretic period collapse
Quang-Nhat Le
In a recent paper, Cristofaro-Gardiner--Li--Stanley [CGLS15] constructed examples of irrational triangles whose Ehrhart functions (i.e. lattice-point count) are polynomials when re…
A continuous analogue of lattice path enumeration
T. Wakhare, C. Vignat, Q. -N. Le +1
Following the work of Cano and Diaz, we consider a continuous analog of lattice path enumeration. This allows us to define a continuous version of any discrete object that counts c…
A projective analogue of Napoleon's and Varignon's theorems
Quang-Nhat Le
What do Napoleon's and Varignon's theorems have in common? We claim that they both are examples of immediately regularizing natural polygon iterations in different planar geometrie…
Macdonald's solid-angle sum for real dilations of rational polygons
Quang-Nhat Le, Sinai Robins
The solid-angle sum of a rational polytope , with was first investigated by I.G. Macdonald. Using our F…
Fourier transforms of polytopes, solid angle sums, and discrete volume
Ricardo Diaz, Quang-Nhat Le, Sinai Robins
Given a real closed polytope , we first describe the Fourier transform of its indicator function by using iterations of Stokes' theorem. We then use the ensuing Fourier transfor…
A family of projectively natural polygon iterations
Quang-Nhat Le
The pentagram map was invented by Richard Schwartz in his search for a projective-geometric analogue of the midpoint map. It turns out that the dynamical behavior of the pentagram…