Geodesic
Lyndon words and transition matrices between elementary, homogeneous and monomial symmetric functions
The electronic journal of combinatorics, Tome 13 (2006)

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Zbl EuDML
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.
DOI : 10.37236/1044
Classification : 05E05, 05A99
Mots-clés : partition, permutations, Lyndon words 
Andrius Kulikauskas; Jeffrey Remmel. Lyndon words and transition matrices between elementary, homogeneous and monomial symmetric functions. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1044
@article{10_37236_1044,
     author = {Andrius Kulikauskas and Jeffrey Remmel},
     title = {Lyndon words and transition matrices between elementary, homogeneous and monomial symmetric functions},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1044},
     zbl = {1087.05063},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1044/}
}
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