Some combinatorial games on integer partitions

Combinatorial games have been studied since the early 20^th century. In 1970, Sato showed that a game introduced by Welter in the 1950's could be viewed as a game on integer partitions. He conjectured that the Sprague-Grundy values of this game are related to the irreducible representations of the symmetric group. This conjecture has since been resolved in the affirmative. I will describe this game as well as some others that can be played on integer partitions. I will mention some results and open questions associated with these games, including their locations in the Conway-Gurvich-Ho classification.

This is joint work with Matjaž Krnc, Peter Muršič, Ina Bašić, Hannah Meit, and a number of other current and former students from my home institution.