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.
The following versions are available:
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: