Let $[r_1, r_2, r_3, \ldots, r_i]$ be an integer parition of a positive integer $n$ in descending order, where $\forall x \in \left(1, 2, \ldots, i\right), r_x \geq 1$. Sato-Welter is played between two players, where the game board represents a partition with previously documented properties. In each move, a player selects a cell $(i, j)$ from the game board; and upon selection, the hook analogous to cell $(i, j)$ gets removed. The removal may create two separate parts in the diagram, which will get immediately merged afterwards. The player who makes the last move wins.
Moves
A visual description of allowed type of moves is given below:
Figure 1 — A move in Sato-Welter
In this picture, upon selection of the $(2, 3)$ cell, the hook associated is getting highlighted. After confirmation, the highlighted hook is removed, and the divided parts are merged.
More
Some research are already waiting on publication approval - please contact Prof. Gottlieb for related queries.
