I am trying to understand the partitions of $S_5$ created by it's conjugacy classes but two sources have two different partitions.

Source 1: enter image description here

Source 2: enter image description here

So, for example, in the first table, the partition for cycle structure ()()()()() i.e. $5$ $1$-cycle is $5+0+0+0+0$ but in the second table it is $1+1+1+1+1$.

Could anyone please help me out?

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    $\begingroup$ Normally partition of an integer composed of only positive whole numbers , we generally don't allow zero as a part of the partition, the first table seems to have errors. Second table is fine though. $\endgroup$ Dec 5 '15 at 2:17

The two sources differ by conjugating the partition, i.e., reading the boxes in the Young diagram horizontally vs reading them vertically. Thus 4+1 in the first source corresponds to 2+1+1+1 in the second, and vica versa. It is just a difference in notation between the two sources.


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