Young's lattice and dihedral symmetries
type: Item
instance of: scholarly article
title: Young's lattice and dihedral symmetries
zbMATH Open document ID: 1001.05120
author: Ruedi Suter
published in: European Journal of Combinatorics
publication date: 2002-12-11T00:00:00Z
review text: The set of all partitions \(\lambda=(\lambda_1,\dots,\lambda_k)\) has a natural graph structure (the Hasse graph) where the partitions are the vertices of the graph and two partitions are connected with an edge if the diagram of one of them can be obtained from the other diagram by adding a box. The author considers the automorphisms of a subgraph \(Y_n\) of the Hasse graph defined by the property that the diagram of \(\lambda\in Y_n\) is contained in a rectangular diagram which is a subset of the diagram of \((n-1,n-2,\dots,2,1)\). The main result is that for \(n\geq 3\) the dihedral group \(D_n\) acts naturally on the graph \(Y_n\) and is isomorphic to its automorphism group.
reviewed by: Vesselin Drensky
Mathematics Subject Classification ID: 05E10
Mathematics Subject Classification ID: 05E25
Mathematics Subject Classification ID: 06A07
zbMATH DE Number: 1740612
zbMATH Keywords: Young tableaux
zbMATH Keywords: Hasse graph
zbMATH Keywords: partially ordered sets
zbMATH Keywords: dihedral groups
MaRDI profile type: Publication
full work available at URL: eujc.2001.0541
OpenAlex ID: W1977146127
Wikidata QID: Q56539283
cites work: Q3947818
cites work: Q4344108
DOI: 10.1006/EUJC.2001.0541
description: scientific article; zbMATH DE number 1740612