Non-crossing linked partitions, the partial order << on NC(n), and the S-transform

Details Non-crossing linked partitions, the partial order << on NC(n), and the S-transform Non-crossing linked partitions, the partial order << on NC(n), and the S-transform

2009-01-09

arxiv.org/abs/0901.1175v2

Mathematics

Operator Algebras

Minor modifications and added references to 1st version. 13 pages, no figures

Scientific paper

The paper establishes a connection between two recent combinatorial developments in free probability: the non-crossing linked partitions introduced by Dykema in 2007 to study the S-transform, and the partial order << on NC(n) introduced by Belinschi and Nica in 2008 in order to study relations between free and Boolean probability. More precisely, one has a canonical bijection between NCL(n) (the set of all non-crossing linked partitions of {1, ..., n}) and the set {(p,q) | p,q in NC(n), p<

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