Non-crossing linked partitions, the partial order << on NC(n), and the S-transform
| dc.creator | Nica, Alexandru | |
| dc.date | 2009-01-09 | |
| dc.date | 2009-01-29 | |
| dc.date.accessioned | 2026-07-07T12:35:05Z | |
| dc.date.available | 2026-07-07T12:35:05Z | |
| dc.description | 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<<q}. As a consequence of this bijection, one gets an alternative description of Dykema's formula expressing the moments of a noncommutative random variable a in terms of the coefficients of the reciprocal S-transform 1/S_a. Moreover, due to the Boolean features of <<, this formula can be simplified to a form which resembles the moment-cumulant formula from c-free probability. | |
| dc.description | Minor modifications and added references to 1st version. 13 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/0901.1175 | |
| dc.identifier | http://arxiv.org/abs/0901.1175 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/217663 | |
| dc.subject | Operator Algebras | |
| dc.subject | Combinatorics | |
| dc.subject | 46L54, 05A18 | |
| dc.title | Non-crossing linked partitions, the partial order << on NC(n), and the S-transform | |
| dc.type | text |