Article

Let Me Tell You My Favorite Lattice-point Problem. . .

Integer Points in Polyhedra—Geometry, Number Theory, Representation Theory, Algebra, Optimization, Statistics
Document Type

Conference Proceeding
Publication Date

1-1-2018
Disciplines

Abstract

This collection was compiled by Bruce Reznick from problems presented at the 2006 AMS/IMS/SIAM Summer Research Conference on Integer points in polytopes. SupposeP Rd is a convex rational d-polyhedron. The solid angle !P(x) of a point x (with respect toP) is a real number equal to the proportion of a small ball centered at x that is contained inP. That is, we let B (x) denote the ball of radius centered at x and dene !P(x) := vol (B (x)\P) volB (x) for all positive suciently small. We note that when x = 2P, !P(x) = 0; when x2P , !P(x) = 1; when x2 @P, 0 < !P(x) < 1. We dene

DOI

10.1090/conm/452
Citation Information

Matthias Beck, Benjamin Nill, Bruce Reznick, Carla Savage, et al.. "Let Me Tell You My Favorite Lattice-point Problem. . ." *Integer Points in Polyhedra—Geometry, Number Theory, Representation Theory, Algebra, Optimization, Statistics*Vol. 452 (2018) p. 179 - 186 ISSN: 978-0-8218-4173-0

Available at: http://works.bepress.com/ivan-soprunov/18/