This material has been published in Séminaire Lotharingien Combin. 34 (1995), Article B34i, 17 pp.

Christian Krattenthaler

Counting nonintersecting lattice paths with respect to weighted turns

(17 pages)

Abstract. We derive enumeration formulas for families of nonintersecting lattice paths with given starting and end points and a given total number of North-East turns. These formulas are important for the computation of Hilbert series for determinantal and pfaffian rings.

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There is an error in the argument in the proof of Theorem 4 on pp. 11/12 that a family of two-rowed arrays with associated permutation not the identity permutation must contain a crossing point: the inequality A(\si(i+1))1 -1<= A(\si(i))1 on page 12 is not true in general. This gap was fixed by Martin Rubey, see his ``Comment on `Counting nonintersecting lattice paths with respect to weighted turns' by Christian Krattenthaler", for which the following versions are available:
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