Vicious walkers, friendly walkers and Young tableaux III: Between two walls

Christian Krattenthaler, Anthony J. Guttmann, Xavier G. Viennot

Published 2002-02-16, updated 2002-07-03Version 2

We derive exact and asymptotic results for the number of star and watermelon configurations of vicious walkers confined to lie between two impenetrable walls, as well as for the analogous problem for $\infty$-friendly walkers. Our proofs make use of results from symmetric function theory and the theory of basic hypergeometric series.