= Locally admissible word for a transition matrix
{title2=$A_{x_0x_1}\cdots A_{x_{n-1}x_n}=1$}
= Locally admissible word
{synonym}
A finite <word over an alphabet> is locally admissible for a zero-one <symbolic transition matrix> if every consecutive pair is permitted. Its length counts symbols, so length $n+1$ corresponds to $n$ transitions. The number with endpoints $i,j$ is $(A^n)_{ij}$ by <matrix multiplication>. Local admissibility does not always imply occurrence in a two-sided <subshift of finite type>: the <matrix> $\begin{pmatrix}0&1\\0&0\end{pmatrix}$ permits the word $(1,2)$ but admits no two-sided <sequence>. If every row and column has a nonzero entry, every locally admissible word extends in both directions.
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