The initial involution patterns of permutations
type: Item
instance of: scholarly article
title: The initial involution patterns of permutations
zbMATH Open document ID: 1111.05003
author: Dongsu Kim
author: Jang Soo Kim
published in: The Electronic Journal of Combinatorics
publication date: 2007-03-12T00:00:00Z
full work available at URL: https://eudml.org/doc/127265
full work available at URL: v14i1r2.html
review text: Summary: For a permutation \(\pi=\pi_1\pi_2\cdots\pi_n \in S_n\) and a positive integer \(i\leq n\), we can view \(\pi=\pi_1\pi_2\cdots\pi_i\) as an element of \(S_i\) by order-preserving relabeling. The \(j\)-set of \(\pi\) is the set of \(i\)'s such that \(\pi=\pi_1\pi_2\cdots\pi_i\) is an involution in \(S_i\). We prove a characterization theorem for \(j\)-sets, give a generating function for the number of different \(j\)-sets of permutations in \(S_n\). We also compute the number of permutations in \(S_n\) with a given \(j\)-set and prove some properties of them.
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 5132836
zbMATH Keywords: generating function
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5132836