Finding The Splitting Numbers of Tiles
Jacob Folks · Furman University Scholar Exchange (Furman University) · 2017
In this research, the bounds of splitting numbers for finite tiles and their characteristics were analyzed. From prior research by Dr. Cooper, it was proved that the lower bound of splitting numbers is 2, and an upper bound is |T|+1, where |T| is the number of elements in a tile. The main result of this research was proving a tighter upper bound that is |T| for all finite tiles T by the use of an algorithm that can split any |T|-covering without fail. This research also proved that translations, reflections, and scalar multiples of tiles have equal splitting numbers. This allows the tiles to be grouped into categories based on their root tile.