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

Authors
Krattenthaler, C Guttmann, AJ Viennot, XG
Citation
C. Krattenthaler et al., Vicious walkers, friendly walkers and Young tableaux: II. With a wall, J PHYS A, 33(48), 2000, pp. 8835-8866
Citations number
51
Categorie Soggetti
Physics
Journal title
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
ISSN journal
03054470 → ACNP
Volume
33
Issue
48
Year of publication
2000
Pages
8835 - 8866
Database
ISI
SICI code
0305-4470(200012)33:48<8835:VWFWAY>2.0.ZU;2-1
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 comb inatorial descriptions of symmetric functions. For the problem of n friendl y walkers, we derive exact asymptotics for the number of stars and watermel ons, both in the absence of a wall and in the presence of a wall.