## k-Dependence on Hexagonal Boards

- Jan. 27, 2017
- 2:30 p.m.
- LeConte 312

## Abstract

Combinatorial chessboard problems are a commonly studied topic in recreational mathematics. Rather than a standard chessboard, we examine one such problem using a rhomboidal board where each space is a hexagon. In particular, taking the standard movements of a king in hexagonal chess, we investigate the maximum number of kings that may be placed on a board so that no king is attacking more than k other kings. We develop both upper and lower bounds for this number for all appropriate values of k.

Collaborators: Robert Doughty, Jessica Gonda, Adriana Morales, Berkeley Reiswig, Josiah Reiswig, Katherine Slyman, and Daniel Pritikin