# Tableau

This is a small game I wrote to demonstrate some of the combinatorics which appears when you study the representation theory of the symmetric group. First you need to choose a weakly decreasing sequence of positive numbers for example 4 3 2 or 5 4 4 1. In representation theory, we call this a partition. You will be presented with a configuration which looks like:

1
2
3
4
5
6
7
8
9

Notice that the numbers increase by 1 as you go along the rows. The aim of the game is to transform the configuration so that the numbers increase by 1 along the columns:

1
4
7
9
2
5
8
3
6

When you click on a number, say n, it will swap n and n+1 as long as they are not in the same row or column. If they are in the same row or column nothing will happen. Also if n is the largest number, then the game will not be happy because there is no n+1 to swap with.