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

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

2001-06-11

arxiv.org/abs/math/0106076v3

in: Algebra, Arithmetic and Geometry with Applications, C. Christensen, C. Bajaj, G. Sundaram and A. Sathaye, eds., Springer-V

Mathematics

Commutative Algebra

28 pages, AmS-LaTeX; an error in the definition of ladder determinantal ring was corrected

Scientific paper

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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