SIR Mathematics Investigation Abstract
COUNTING NUMBER OF LATTICE POINTS INSIDE A 3-D TETRAHEDRON
Presenter:
Letian Zhang, Illinois Mathematics and Science Academy, 1500 West Sullivan Road, Aurora, IL, 60506
Mentor:
Dr. Stephen Yau, University of Illinois at Chicago
Abstract:
The counting of lattice points inside a 3-dimensional tetrahedron has been an intriguing problem for years. For the tetrahedrons with integer coordinates, Erhart has found a polynomial that corresponds to the number of lattice points inside a n-dimensional tetrahedron. However after n>2, Ehrhart's polynomial cannot be expressed explicitly. The goal of our mentorship is to find explicit bounds for the number of lattice points inside a 3-dimensional tetrahedron.