Abstract by Josh Linnell
Lattice Simplex Covering Properties
Suppose we are given a lattice L, and want to know if we can cover with a given simplex. If we construct a tile for the lattice, it is obvious we will get a cover with a density of one using the tile. If we then choose a simplex that contains that tile, the simplex will also cover. We will examine the combinatorial properties of the tiles for a lattice and their effect on the covering density. Specifically, we will examine the combinatorial properties of tile types generated by the subtraction construction.