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

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

2000-06-23

arxiv.org/abs/cond-mat/0006367v2

J.Phys.A33:8835-8866,2000

Physics

Condensed Matter

Statistical Mechanics

35 pages, AmS-LaTeX; Definitions of n-friendly walkers clarified; the statement of Theorem 4 and its proof were corrected

Scientific paper

10.1088/0305-4470/33/48/318

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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