Column Row Impartial Split (CRIS)

Integer Parition Combinatorial Game

Let $n$ be a positive integer, and $ \left( a^{a'}, b^{b'}, \ldots, i^{i'} \right)$ be an integer partiton of $n$ where $a > b > \cdots > i$. CRIS is an impartial game --- where the partition is visually presented with an Young Diagram --- and users may delete any row or column remaining in the board. Fragment parts might appear in the board; in such cases, each fragment will be "independent," meaning a move in one wouldn't impact others. The player who makes the last move wins. The program demonstrating this game was algorithmically bases on JavaScript where Breadth First Search and fractioned Grundy values were used to induce perfect play.

Moves

There are two types of move in CRIS, which functions as below:

More

Some research are already waiting on publication approval - please contact Prof. Gottlieb for related queries.