  A composition of a nonnegative integer (n) is a sequence of positive integers
whose sum is (n). A composition is palindromic if it is unchanged when its
terms are read in reverse order. We provide a generating function for the
number of occurrences of arbitrary segmented partially ordered patterns among
compositions of (n) with a prescribed number of parts. These patterns
generalize the notions of rises, drops, and levels studied in the literature.
We also obtain results enumerating parts with given sizes and locations among
compositions and palindromic compositions with a given number of parts. Our
results are motivated by "encoding by restricted permutations," a relatively
undeveloped method that provides a language for describing many combinatorial
objects. We conclude with some examples demonstrating bijections between
restricted permutations and other objects.
