Geodesic
Canonical characters on simple graphs
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 1, pp. 107-113

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MR Zbl
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 formulas and properties of characters are used to derive some interesting numerical identities relating multinomial and central binomial coefficients.
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 formulas and properties of characters are used to derive some interesting numerical identities relating multinomial and central binomial coefficients.
DOI : 10.1007/s10587-013-0007-3
Classification : 05C25, 05E05, 16T30
Keywords: Hopf algebra; simple graph; quasi-symmetric function; character 
Stojadinović, Tanja. Canonical characters on simple graphs. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 1, pp. 107-113. doi: 10.1007/s10587-013-0007-3
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