Avoiding permutations and the Narayana numbers

Youngja Park; Seungkyung Park

doi:10.4134/JKMS.2013.50.3.529

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

QR
Code

Article

HOME

ALL ARTICLES

View

J. Korean Math. Soc. 2013; 50(3): 529-541

Printed May 1, 2013

https://doi.org/10.4134/JKMS.2013.50.3.529

Avoiding permutations and the Narayana numbers

Youngja Park and Seungkyung Park

Yonsei University, Yonsei University

Abstract

Go to

Abstract

We study $132$ avoiding permutations that also avoid $(2r+1)(2r+2)\cdots 12$ but contain $(2r-1)(2r)\cdots 12$ pattern. We find an identity between the number of these permutations and the \textit{Narayana number}. We also present relations between 132 avoiding permutations and polygon dissections. Finally, a generalization of these permutations is obtained.

Keywords: avoiding permutation, Narayana number, dissection number

MSC numbers: 05A15