Vicious walkers, friendly walkers and Young tableaux. II: With a wall. (English) Zbl 0970.82016
Summary: 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.
For Part I, see A. J. Guttman, A. L. Owczarek and X. G. Viennot [ibid. 31, 8123-8135 (1998; Zbl 0930.05098)].
For Part I, see A. J. Guttman, A. L. Owczarek and X. G. Viennot [ibid. 31, 8123-8135 (1998; Zbl 0930.05098)].
MSC:
| 82B41 | Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics |
| 05E10 | Combinatorial aspects of representation theory |
| 82B23 | Exactly solvable models; Bethe ansatz |
Citations:
Zbl 0930.05098Online Encyclopedia of Integer Sequences:
Triangle T(n,k) read by rows: related to David G. Cantor’s sigma function.Upper triangle of Catalan Number Wall.
