I would like to express $$\text{The set of vectors}\,\{\boldsymbol p_1, \boldsymbol p_2, \ldots, \boldsymbol p_{24}\}\,\text{is the permutations of}\,\begin{bmatrix}A&B&C&D\end{bmatrix}$$ $$\text{e.g.:} \boldsymbol p_1=\{A,B,C,D\}, \boldsymbol p_2 = \{A, B, D, C\}, \text{etc.}$$in a more compact manner. Is there a special notation for this?
Compact notation to express all permutation of a set
combinatoricsnotationpermutations
Best Answer
As suggested in the comments, you could do $S_4$. However, if it's important to you that these are permutations of $A, B, C, D$ specifically and not just any set with 4 elements, then you could also say $\Sigma(\{A, B, C, D\})$. In general, $\Sigma(X)$ refers to all the permutations of the set $X$.