A determinantal formula for the Hilbert series of one-sided ladder determinantal rings
Commutative Algebra
2007-05-23 v3 Algebraic Geometry
Combinatorics
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
Cite
@article{arxiv.math/0106076,
title = {A determinantal formula for the Hilbert series of one-sided ladder determinantal rings},
author = {Christian Krattenthaler and Martin Rubey},
journal= {arXiv preprint arXiv:math/0106076},
year = {2007}
}
Comments
28 pages, AmS-LaTeX; an error in the definition of ladder determinantal ring was corrected