Generalized permutation patterns -- a short survey

Details Generalized permutation patterns -- a short survey Generalized permutation patterns -- a short survey

2008-01-16

arxiv.org/abs/0801.2412v2

Mathematics

Combinatorics

11 pages. Added a section on asymptotics (Section 8), added more examples of barred patterns equal to generalized patterns (Se

Scientific paper

An occurrence of a classical pattern p in a permutation \pi is a subsequence of \pi 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.

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