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

2009/01/09 by Alexandru Nica, Nica, Alexandru
Mathematics · #05A18 #46L54 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Operator Algebras (math.OA) #Random Matrices and Applications

paper · doi:10.48550/arxiv.0901.1175

openalex publication_date 2009/01/09 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

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 &lt;&lt; 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&lt;

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