Summary: An occurrence of a classical pattern \(p\) in a permutation \(\pi\) is a subsequence of \(p\) 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.
For the entire collection see [Zbl 1190.05001].