Motivation: This post.
$K \subset S_n, \langle K \rangle =G \leq S_n$. We can create a Representation Matrix $M$ from $K$ that represnts $G$ (Furst. Hopcroft, Luks).
Question: Is $M$ unique for a fixed $K$ i.e. can we generat two different Representation Matrices from same $K$ ?
Edit: Each row $i$ of $M$ represents the complete right traversal set of $G_i$ in $G_{i-1} $ where $G_i$ is the pointwise stabilizer of $\{ 1,2...i\}$ and $G_0=G$.