Vicious walkers, friendly walkers and Young tableaux II: With a wall

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

Published 2000-06-23, updated 2000-11-07Version 2

We derive new results for the number of star and watermelon configurations of vicious walkers in the presence of an impenetrable wall by showing that these follow from standard results in the theory of Young tableaux, and combinatorial descriptions of symmetric functions. For the problem of $n$-friendly walkers, we derive exact asymptotics for the number of stars and watermelons both in the absence of a wall and in the presence of a wall.