Hypergraph Nim

Nim is an impartial game in which two players take turns choosing a pile and removing a positive tokens from it, with the player making the last move winning. Impartial games are solved by finding which positions are winning and losing, the winning move makes your winning position into a losing position for the opponent. A generalization of winning and losing positions is called the Sprague-Grundy function which partitions positions even further and is needed to know how to play the sum of games. Hypergraph Nim is a new generalization of the game Nim in which instead of a single pile we chose multiple, with our choice of piles denoted by a hypergraph. In this talk we will take a look at the Sprague-Grundy function of Hypergraph Nim.