Lyndon words and transition matrices between elementary, homogeneous and monomial symmetric functions
The electronic journal of combinatorics, Tome 13 (2006)
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.
@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/}
}
TY - JOUR AU - Andrius Kulikauskas AU - Jeffrey Remmel TI - Lyndon words and transition matrices between elementary, homogeneous and monomial symmetric functions JO - The electronic journal of combinatorics PY - 2006 VL - 13 UR - http://geodesic.mathdoc.fr/articles/10.37236/1044/ DO - 10.37236/1044 ID - 10_37236_1044 ER -
%0 Journal Article %A Andrius Kulikauskas %A Jeffrey Remmel %T Lyndon words and transition matrices between elementary, homogeneous and monomial symmetric functions %J The electronic journal of combinatorics %D 2006 %V 13 %U http://geodesic.mathdoc.fr/articles/10.37236/1044/ %R 10.37236/1044 %F 10_37236_1044
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
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