arXiv subjects

Xavier G. Viennot

Publications and source records attributed to Xavier G. Viennot.

2 recordsLinked to original sources

arXiv2002

Vicious walkers, friendly walkers and Young tableaux III: Between two walls

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 for the analogous problem for $\infty$-friendly walkers. Our proofs make use of results from symmetric function theory and the theory of basic hypergeometric series.

cond-mat.stat-mech↗

arXiv2000

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

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.

cond-mat.stat-mech↗