Lyndon words and transition matrices between elementary, homogeneous and monomial symmetric functions
type: Item
instance of: scholarly article
title: Lyndon words and transition matrices between elementary, homogeneous and monomial symmetric functions
zbMATH Open document ID: 1087.05063
author: Andrius Kulikauskas
author: Jeffrey Remmel
published in: The Electronic Journal of Combinatorics
publication date: 2006-03-22T00:00:00Z
full work available at URL: https://eudml.org/doc/125958
full work available at URL: v13i1r18.html
review text: Summary: Let \(h_\lambda\), \(e_\lambda\), and \(m_\lambda\) denote the homogeneous symmetric function, the elementary symmetric function and the monomial symmetric function associated with the partition \(\lambda\) respectively. We give combinatorial interpretations for the coefficients that arise in expanding \(m_\lambda\) in terms of homogeneous symmetric functions and the elementary symmetric functions. Such coefficients are interpreted in terms of certain classes of bi-brick permutations. The theory of Lyndon words is shown to play an important role in our interpretations.
Mathematics Subject Classification ID: 05E05
Mathematics Subject Classification ID: 05A99
zbMATH DE Number: 5014315
zbMATH Keywords: partition
zbMATH Keywords: permutations
zbMATH Keywords: Lyndon words
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5014315