0
votes
0answers
120 views

Algebraic proof of Ehrhart's theorem

Let $P \subset \mathbb{R}^d$ be a $d$-dimensional polytope, where all vertices lie on integral coordinates, and let $L(P,n)$ denote the number of integral lattice points contained in the scaled ...
8
votes
1answer
330 views

“Center-of-Mass” of lattice polygons (generalization of Pick's theorem)

Call a polygon with integer coordinates (in the Euclidean plane) a 'lattice polygon'. Pick's Theorem allows you to efficiently compute the number of lattice points inside this polygon given just its ...
3
votes
1answer
313 views

Which internal angles can a lattice polygon have?

I am wondering if for a lattice polygon an internal angle can take any value? If no which ones not and why? I guess there will be some restrictions due to the discrete nature of the grid but I am ...
16
votes
5answers
999 views

Pick's Theorem on a triangular (or hex) grid

Pick's theorem says that given a square grid (that is, all points in the plane with integer coordinates) and a polygon without holes and non selt-intersecting whose vertices are grid points, its area ...