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

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

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Commutative Algebra, Algebraic Geometry, Combinatorics, 05A15 13C40 (Primary) 05A19 13F50 13H10 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/61625

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0106076
 http://arxiv.org/abs/math/0106076
 in: Algebra, Arithmetic and Geometry with Applications, C. Christensen, C. Bajaj, G. Sundaram and A. Sathaye, eds., Springer-Verlag, New York, 2003, pp. 525-552.

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arXiv