Ehrhart's Polynomial for Equilateral Triangles in Z3
 Citation data:

Centre for Discrete Mathematics and Computing
 Publication Year:
 2013

 Bepress 1

 Bepress 1
 Repository URL:
 https://csuepress.columbusstate.edu/bibliography_faculty/388
 Author(s):
 Tags:
 Mathematics
article description
In this paper we calculate the Ehrhart’s polynomial associated with a 2dimensional regular polytope (i.e. equilateral triangles) in Z3. The polynomial takes a relatively simple form in terms of the coordinates of the vertices of the triangle. We give some equivalent formula in terms of a parametrization of these objects which allows one to construct equilateral triangles with given properties. In particular, we show that given a prime number p which is equal to 1 or −5 (mod 8), there exists an equilateral triangle with integer coordinates whose Ehrhart polynomial is L(t) = (pt + 2)(t + 1)/2, t ∈ N.