Geodesic
Chromatic polynomials of graphs from Kac-Moody algebras
Journal of Algebraic Combinatorics, Tome 41 (2015) no. 4, pp. 1133-1142.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We give a new interpretation of the chromatic polynomial of a simple graph $G$ in terms of the Kac-Moody Lie algebra $\mathfrak {g}$ with Dynkin diagram $G$. We show that the chromatic polynomial is essentially the $q$-Kostant partition function of $\mathfrak {g}$ evaluated on the sum of the simple roots. Applying the Peterson recurrence formula for root multiplicities of $\mathfrak {g}$, we obtain a new realization of the chromatic polynomial as a weighted sum of paths in the bond lattice of $G$.
Classification : 05C31, 17B10, 17B67, 05C15, 05C38
Keywords: chromatic polynomial, $q$-Kostant partition function, Kac-Moody algebras 
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     title = {Chromatic polynomials of graphs from {Kac-Moody} algebras},
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Venkatesh, R.; Viswanath, Sankaran. Chromatic polynomials of graphs from Kac-Moody algebras. Journal of Algebraic Combinatorics, Tome 41 (2015) no. 4, pp. 1133-1142. http://geodesic.mathdoc.fr/item/JAC_2015__41_4_a0/