TY - JOUR
T1 - Let Me Tell You My Favorite Lattice-point Problem. . .
AU - Beck, Matthias
AU - Nill, Benjamin
AU - Reznick, Bruce
AU - Savage, Carla
AU - Soprunov, Ivan
AU - Xu, Zhiqiang
PY - 2018/1/1
Y1 - 2018/1/1
N2 - 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
AB - 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
UR - https://engagedscholarship.csuohio.edu/scimath_facpub/281
UR - http://www.ams.org/books/conm/452/
U2 - 10.1090/conm/452
DO - 10.1090/conm/452
M3 - Article
VL - 452
JO - Integer Points in Polyhedra—Geometry, Number Theory, Representation Theory, Algebra, Optimization, Statistics
JF - Integer Points in Polyhedra—Geometry, Number Theory, Representation Theory, Algebra, Optimization, Statistics
ER -