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, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Springer-Verlag. This material may not be copied or reposted without explicit permission.

Martin Rubey and Christian Krattenthaler

A determinantal formula for the Hilbert series of one-sided ladder determinantal rings

(28 pages)

Abstract. 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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