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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 The paper under review is a survey of recent results in the area of permutation patterns and includes many unpublished results.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
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