Partition of n: A partition of the integer n is a sequence of positive integers , satisfy: .
Young Diagram: A partition is represented graphically by a Young Diagram which consists of squares arranged in rows, the th one of which contains squares.
Theorem: The number of distinct Young diagrams for any given n is equal to the number of classes of -which is, in turn, equal the number of inequivalent irreducible representations of
Young Tableau: A Young tableau is one in which the number appear in order from left to right and from the top row to the bottom row.
Normal Young Tableau: is one in which the numbers appear in order from left to right and from the top row to the bottom row.
Standard Young Tableau: is one in which the numbers in each row appear increasing (not necessarily in strict order) to the right and those in each column appear increasing to the bottom.
The classes of group can be characterized by cycle structure as it is said in Section 2.3. If we have 1-cycle, 2-cycle, etc., the relationship between and is , as it is illustrated in the figure.
The relationship between young diagram and cycles