# Permutations Containing and Avoiding \$ extit{123}\$ and \$ extit{132}\$ Patterns

Permutations Containing and Avoiding \$ extit{123}\$ and \$ extit{132}\$ Patterns - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

1 Department of Mathematics Hamilton NY

Abstract : We prove that the number of permutations which avoid 132-patterns and have exactly one 123-pattern, equals \$n-22^{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-3n-42^{n-5}\$, for \$n \ge 5\$.

Keywords : Patterns Words

Autor: Aaron Robertson -

Fuente: https://hal.archives-ouvertes.fr/

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