On the number of absolutely indecomposable representations of a quiver

A conjecture of Kac states that the constant coefficient of the polynomial counting the number of absolutely indecomposable representations of a quive r over a finite field is equal to the multiplicity of the corresponding roo t in the associated Kac-Moody Lie algebra. In this paper we give a combinat orial reformulation of Kac's conjecture in terms of a property of q-multino mial coefficients. As a side result we give a formula for certain inverse K ostka-Foulkes polynomials. (C) 1999 Academic Press.