Hopf algebras of words and overlapping shuffle algebra (Retracted)
Olivera Marković (2007)
Kragujevac Journal of Mathematics
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Olivera Marković (2007)
Kragujevac Journal of Mathematics
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Bergeron, N., Hohlweg, C., Rosas, M., Zabrocki, M. (2006)
The Electronic Journal of Combinatorics [electronic only]
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Tanja Stojadinović (2013)
Czechoslovak Mathematical Journal
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A multiplicative functional on a graded connected Hopf algebra is called the character. Every character decomposes uniquely as a product of an even character and an odd character. We apply the character theory of combinatorial Hopf algebras to the Hopf algebra of simple graphs. We derive explicit formulas for the canonical characters on simple graphs in terms of coefficients of the chromatic symmetric function of a graph and of canonical characters on quasi-symmetric functions. These...
Bergeron, François, Lauve, Aaron (2010)
The Electronic Journal of Combinatorics [electronic only]
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Szczesny, Matt (2010)
The Electronic Journal of Combinatorics [electronic only]
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Bell, J., Garsia, A.M., Wallach, N. (2005)
The Electronic Journal of Combinatorics [electronic only]
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Bergeron, François, Biagioli, Riccardo (2006)
The Electronic Journal of Combinatorics [electronic only]
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Daily, Marilyn, Lada, Tom
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Summary: We show that the symmetrization of a brace algebra structure yields the structure of a symmetric brace algebra. We also show that the symmetrization of the natural brace structure on coincides with the natural symmetric brace structure on , the direct sum of spaces of antisymmetric maps .