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

By Christian Krattenthaler, Anthony John Guttmann, X. Viennot. 2000

150 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a6bfbd53c0bf23dc491950c443bdc05446c0ca3d

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In Discrete Mathematics and Combinatorics

In Statistics and Probability

Citations in the corpus

Plane partitions in the work of Richard Stanley and his school (2015, background): “), enumeration of integer points in polytopes and commutative algebra (cf. [12, 79, 17] and the references therein), enumeration of matchings in graphs (cf. [62, 66]), and to statistical physics (cf. [39, 61]). In brief, the theory of plane partitions oﬀered challenging conjectures (most of them sol”
Nonintersecting Brownian Excursions (2006, methodology): “This heuristic definition of this Markov process requires elaboration [11, 21] since such paths have zero Wiener measure.”