Vicious walkers, friendly walkers, and Young tableaux. III: Between two walls. (English) Zbl 1016.82017
Summary: 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 co-friendly walkers. Our proofs make use of results from symmetric function theory and the theory of basic hypergeometric series.
For Part II, see J. Phys. A, Math. Gen. 33, 8835-8966 (2000; Zbl 0970.82016).
For Part II, see J. Phys. A, Math. Gen. 33, 8835-8966 (2000; Zbl 0970.82016).
MSC:
| 82B41 | Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics |
| 05E05 | Symmetric functions and generalizations |
| 05E10 | Combinatorial aspects of representation theory |
| 33D80 | Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics |
