Abstract
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 corresponding results for the analogous problem of ∞-friendly walkers. Our proofs make use of results from symmetric function theory and the theory of basic hypergeometric series.
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Krattenthaler, C., Guttmann, A.J. & Viennot, X.G. Vicious Walkers, Friendly Walkers, and Young Tableaux. III. Between Two Walls. Journal of Statistical Physics 110, 1069–1086 (2003). https://doi.org/10.1023/A:1022192709833
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DOI: https://doi.org/10.1023/A:1022192709833