Canonical characters on simple graphs

Stojadinović, Tanja. "Canonical characters on simple graphs." Czechoslovak Mathematical Journal 63.1 (2013): 107-113. <http://eudml.org/doc/252547>.

@article{Stojadinović2013,
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.},
author = {Stojadinović, Tanja},
journal = {Czechoslovak Mathematical Journal},
keywords = {Hopf algebra; simple graph; quasi-symmetric function; character; multiplicative functional; graded connected Hopf algebra; simple graph; quasi-symmetric function; even character; odd character; chromatic symmetric functions; quasi-symmetric functions; identities; multinomial coefficients; central binomial coefficients},
language = {eng},
number = {1},
pages = {107-113},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Canonical characters on simple graphs},
url = {http://eudml.org/doc/252547},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Stojadinović, Tanja
TI - Canonical characters on simple graphs
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 1
SP - 107
EP - 113
AB - 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.
LA - eng
KW - Hopf algebra; simple graph; quasi-symmetric function; character; multiplicative functional; graded connected Hopf algebra; simple graph; quasi-symmetric function; even character; odd character; chromatic symmetric functions; quasi-symmetric functions; identities; multinomial coefficients; central binomial coefficients
UR - http://eudml.org/doc/252547
ER -