Séminaire Lotharingien de Combinatoire, B34i (1995), 17pp.

Christian Krattenthaler

Counting nonintersecting lattice paths with turns

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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Comment by Martin Rubey

Martin Rubey points out that 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 contains an error: the inequality A(\si(i+1))1 -1<= A(\si(i))1 on page 12 is not true in general. He provides the following fix: