Vicious walkers, friendly walkers and Young tableaux II: With a wall
Statistical Mechanics
2008-11-26 v2 High Energy Physics - Lattice
High Energy Physics - Theory
Mathematical Physics
Combinatorics
math.MP
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 combinatorial descriptions of symmetric functions. For the problem of -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.
Keywords
Cite
@article{arxiv.cond-mat/0006367,
title = {Vicious walkers, friendly walkers and Young tableaux II: With a wall},
author = {Christian Krattenthaler and Anthony J. Guttmann and Xavier G. Viennot},
journal= {arXiv preprint arXiv:cond-mat/0006367},
year = {2008}
}
Comments
35 pages, AmS-LaTeX; Definitions of n-friendly walkers clarified; the statement of Theorem 4 and its proof were corrected