Notation for the set of all sequences of coin tosses of length n

Question

I need to denote the set of all coin toss sequences of length $n$, but I'm not sure what the proper notation is. My guess is:

$$ S = \{x_1 x_2 ... x_n \,|\, x_i \in \{H, T\}\} $$

Is that correct? Seems like there might be a convention for this.

Answer 1

As Gerry Myerson says, the notation you seek is the $n$-ary Cartesian power of the set $\{\mathcal H,\mathcal T\}$

$$\{\mathcal H, \mathcal T\}^n = \Big\{ (x_1, .. , x_n) : \forall i\in \{1,..,n\}~\big(x_i\in\{\mathcal H,\mathcal T\}\big)\Big\} \\[1ex] = \underbrace{\{\mathcal H, \mathcal T\}\times \{\mathcal H, \mathcal T\}\times \cdots \times \{\mathcal H, \mathcal T\}}_{\text{$n$ times}}\;\;$$