Random 3-noncrossing partitions

Details Random 3-noncrossing partitions Random 3-noncrossing partitions

2009-10-14

arxiv.org/abs/0910.2608v1

Mathematics

Combinatorics

17 pages, 7 figures

Scientific paper

In this paper, we introduce polynomial time algorithms that generate random 3-noncrossing partitions and 2-regular, 3-noncrossing partitions with uniform probability. A 3-noncrossing partition does not contain any three mutually crossing arcs in its canonical representation and is 2-regular if the latter does not contain arcs of the form $(i,i+1)$. Using a bijection of Chen {\it et al.} \cite{Chen,Reidys:08tan}, we interpret 3-noncrossing partitions and 2-regular, 3-noncrossing partitions as restricted generalized vacillating tableaux. Furthermore, we interpret the tableaux as sampling paths of Markov-processes over shapes and derive their transition probabilities.

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