Generalized permutation patterns - a short survey

An occurrence of a classical pattern p in a permutation π is a
subsequence of π whose letters are in the same relative order (of size) as those
in p. In an occurrence of a generalized pattern, some letters of that subsequence
may be required to be adjacent in the permutation. Subsets of permutations
characterized by the avoidance—or the prescribed number of occurrences—
of generalized patterns exhibit connections to an enormous variety of other
combinatorial structures, some of them apparently deep. We give a short
overview of the state of the art for generalized patterns.