## The patterns of permutations.(English)Zbl 1028.05002

For $$\tau \in S_k$$ and $$\sigma \in S_n$$, $$k \leq n$$, the pattern $$\tau$$ occurs in the permutation $$\sigma$$ if there exist $$\sigma_{i_{1}}, \sigma_{i_{2}},\dots, \sigma_{i_{k}}$$ for $$i_1< i_2<\cdots < i_k$$ such that $$\sigma_{i_{a}} < \sigma_{i_{b}}$$ if and only if $$\tau_{a}<\tau_{b}$$. The paper under review is a survey of recent results in the area of permutation patterns and includes many unpublished results.

### MSC:

 05A05 Permutations, words, matrices

### Keywords:

permutations; pattern avoidance
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