What is a permutation pattern? The wikipedia entry for permutation pattern gives this as an example:

For example, in the permutation π = 391867452, π1=3 and π9=2. A permutation π is said to contain the permutation σ if there exists a subsequence of (not necessarily consecutive) entries of π that has the same relative order as σ, and in this case σ is said to be a pattern of π, written σ ≤ π. Otherwise, π is said to avoid the permutation σ. For example, the permutation π = 391867452 contains the pattern σ = 51342, as can be seen in the highlighted subsequence of π = 391867452 (or π = 391867452 or π = 391867452). Each subsequence (91674, 91675, 91672) is called a copy, instance, or occurrence of σ. Since the permutation π = 391867452 contains no increasing subsequence of length four, π avoids 1234.

In that example, is a pattern of 51342 the same as a pattern of, say, 62453 or 92483?  I mean, is it the just the the increase/decrease as well as the relative magnitude of each digit with respect to every other digit in the sequence that makes a pattern? Or must a pattern be "reduced" so that the value of the lowest digit in the pattern is 1 and the difference between the two values in the "sort" of the pattern is no more than 1?

Typically a pattern of length $k$ is written as a permutation of $\{1,\dotsc,k\}$. This has at least two advantages. First, the pattern itself is a permutation of a simple set, making things simpler. Second, it gives each pattern a unique representation. Sure you could define patterns to include $413$ (in place of or in addition to $312$) but that does not seem to add anything to its utility.
