This material has been published in Trans. Amer. Math. Soc. 351 (1999), 1015-1042, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by the American Mathematical Society. This material may not be copied or reposted without explicit permission.

Christian Krattenthaler

A remarkable formula for counting nonintersecting lattice paths in a ladder with respect to turns

(29 pages)

Abstract. We prove a formula, conjectured by Conca and Herzog, for the number of all families of nonintersecting lattice paths with certain starting and end points in a region that is bounded by an upper ladder. Thus we are able to compute explicitly the Hilbert series for certain one-sided ladder determinantal rings.

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