This material has been published in J. Phys. A: Math. Gen. 33 (2000), 8835-8866, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by the Institute of Physics. This material may not be copied or reposted without explicit permission.

Christian Krattenthaler, Tony Guttmann and Xavier Viennot

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

(35 pages)

Abstract. 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.

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