This material has been published in
"Algebra, Arithmetic and Geometry
with Applications," C. Christensen, G. Sundaram, A. Sathaye and C. Bajaj,
eds., Springer-Verlag, New York, 2004, pp. 525-552,
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and Christian Krattenthaler
A determinantal formula for the
Hilbert series of one-sided ladder determinantal
We give a formula that expresses the Hilbert series of one-sided ladder
determinantal rings, up to a trivial factor, in form of a determinant.
This allows the convenient computation of these Hilbert series.
The formula follows from a determinantal formula for a generating
function for families of nonintersecting lattice paths that stay
inside a one-sided ladder-shaped region, in which the paths
are counted with respect to turns.
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