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Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 1999

Permutations Containing and Avoiding $\textit{123}$ and $\textit{132}$ Patterns

Abstract

We prove that the number of permutations which avoid 132-patterns and have exactly one 123-pattern, equals $(n-2)2^{n-3}$, for $n \ge 3$. We then give a bijection onto the set of permutations which avoid 123-patterns and have exactly one 132-pattern. Finally, we show that the number of permutations which contain exactly one 123-pattern and exactly one 132-pattern is $(n-3)(n-4)2^{n-5}$, for $n \ge 5$.

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Dates and versions

hal-00958933 , version 1 (13-03-2014)

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Aaron Robertson. Permutations Containing and Avoiding $\textit{123}$ and $\textit{132}$ Patterns. Discrete Mathematics and Theoretical Computer Science, 1999, Vol. 3 no. 4 (4), pp.151-154. ⟨10.46298/dmtcs.261⟩. ⟨hal-00958933⟩

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