A Determinantal Formula for the Hilbert Series of One-sided Ladder Determinantal Rings

Christian Krattenthaler and Martin Rubey

A chapter in Algebra, Arithmetic and Geometry with Applications, 2004, pp 525-551 from Springer

Abstract: 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.

Keywords: Young Tableau; Hilbert Series; Hilbert Function; Schubert Variety; Lattice Path (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18487-1_30

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DOI: 10.1007/978-3-642-18487-1_30

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