Robinson-Schensted correspondence for symmetric group:S3

This article describes the Robinson-Schensted correspondence in detail for specific information about::symmetric group:S3.

Summary
The rest of the article describes in detail how to obtain the position and shape tableaux for each permutation.

Identity permutation
The identity permutation on $$\{ 1,2,3 \}$$ is given by the one-line notation 123. Here is how the position and shape tableau are constructed, letter by letter:

Transposition $$(1,2)$$
In one-line notation, this transposition is written as 213. Here is how the position and shape tableaux are constructed, letter by letter:

Transposition $$(2,3)$$
In one-line notation, the transposition is written as 132. Here is how the position and shape tableaux are constructed, letter by letter:

3-cycle $$(1,2,3)$$
In one-line notation, the 3-cycle is written as 231. Here is how the position and shape tableaux are constructed, letter by letter:

3-cycle $$(1,3,2)$$
In one-line notation, the 3-cycle is written as 312. Here is how the position and shape tableaux are constructed, letter by letter:

Transposition $$(1,3)$$
In one-line notation, the transposition is written as 321. Here is how the position and shape tableaux are constructed, letter by letter: