Czechoslovak Mathematical Journal, Vol. 63, No. 1, pp. 107-113, 2013

Canonical characters on simple graphs

Tanja Stojadinović

Tanja Stojadinović, Belgrade University, Faculty of Mathematics, Studentski trg 16, 11000 Belgrade, Serbia, e-mail: tanjas@matf.bg.ac.rs

Abstract: 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.

Keywords: Hopf algebra, simple graph, quasi-symmetric function, character

Classification (MSC 2010): 05C25, 16T30, 05E05


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