  We define sequence patterns of length $n$ and level $\ell$ to be equivalence
classes of sequences that have $n$ elements from the set of $\ell$ integer
symbols $\{1,2,\ldots,\ell\}$ with no restriction on repetition, where the
equivalence relation is induced by symbol relabeling without swapping positions
of symbols. We define a distance for a set of $k$ sequence patterns of length
$n$ and level $\ell$ by generalizing the Hamming distance between sequences. We
compute the maximal distance for $k$ sequence patterns of length $n$ and level
$\ell$ and demonstrate how to calculate the exact distance between a pair of
length-$n$ level-$\ell$ sequence patterns.
