On avoidance of V- and ^-patterns in permutations

Kitaev, Sergey and Pyatkin, Artem (2010) On avoidance of V- and ^-patterns in permutations. Ars Combinatoria, 97. pp. 203-215.

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Abstract

We study V- and ^-patterns which generalize valleys and peaks, as well as increasing and decreasing runs, in permutations. A complete classi¯cation of permutations (multi)-avoiding V- and ¤-patterns of length 4 is given. We also establish a connection between restricted permutations and matchings in the coronas of complete graphs.