Lyndon Words and Transition Matrices between Elementary, Homogeneous and Monomial Symmetric Functions

Let h, e, and m denote the homogeneous symmetric function, the elementary symmetric function and the monomial symmetric function associated with the partition respectively. We give combinatorial interpretations for the coefficients that arise in expanding m 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.

• Type: Journal
• Year: 2006
• Where: COMBINATORICS
• Authors: Andrius Kulikauskas, Jeffrey B. Remmel
• Keywords: COMBINATORICS 2006, Elementary Symmetric Functions, Homogeneous Symmetric Functions, Symmetric Functions