Pattern avoidance and Young tableaux
type: Item
instance of: scholarly article
title: Pattern avoidance and Young tableaux
zbMATH Open document ID: 1355.05270
author: Zhousheng Mei
author: Suijie Wang
published in: The Electronic Journal of Combinatorics
publication date: 2017-02-17T00:00:00Z
full work available at URL: v24i1p6
review text: Summary: This paper extends Lewis's bijection [\textit{J. B. Lewis}, J. Comb. Theory, Ser. A 118, No. 4, 1436--1450 (2011; Zbl 1231.05286)] to a bijection between a more general class \(\mathcal{L}(n,k,I)\) of permutations and the set of standard Young tableaux of shape \(\langle (k+1)^n\rangle\), so the cardinality \[ |\mathcal{L}(n,k,I)|=f^{(k+1)^{n}\rangle}, \] is independent of the choice of \(I\subseteq [n]\). As a consequence, we obtain some new combinatorial realizations and identities on Catalan numbers. In the end, we raise a problem on finding a bijection between \(\mathcal{L}(n,k,I)\) and \(\mathcal{L}(n,k,I')\) for distinct \(I\) and \(I'\).
Mathematics Subject Classification ID: 05E10
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 6686259
zbMATH Keywords: pattern avoidance
zbMATH Keywords: Young tableaux
zbMATH Keywords: Catalan numbers
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6686259