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Vicious walkers, friendly walkers and Young tableaux II: With a wall | | Christian Krattenthaler
; Anthony J. Guttmann
; Xavier G. Viennot
; | | Date: |
23 Jun 2000 | | Journal: | J.Phys. A33 (2000) 8835-8866 | | Subject: | Statistical Mechanics; Mathematical Physics; Combinatorics MSC-class: 17B20 (Primary) 05A15 05E05 05E10 82B20 82B23 (Secondary) | cond-mat.stat-mech hep-lat hep-th math-ph math.CO math.MP | | Affiliation: | Universität Wien), Anthony J. Guttmann (University of Melbourne) and Xavier G. Viennot (Université Bordeaux 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 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. | | Source: | arXiv, cond-mat/0006367 | | Services: | Forum | Review | PDF | Favorites | |
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