Non-crossing linked partitions and multiplication of free random variables

2008/12/11 by Mihai Popa, Popa, Mihai
Computer Science · Mathematics · #05A10 #46L54 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Operator Algebras (math.OA) #Random Matrices and Applications #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.0812.2064

openalex publication_date 2008/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The material gives a new combinatorial proof of the multiplicative property of the S-transform. In particular, several properties of the coefficients of its inverse are connected to non-crossing linked partitions and planar trees.

Related

• Non-crossing linked partitions, the partial order << on NC(n), and the S-transform
• Linked Partitions and Linked Cycles
• The S-transform in arbitrary dimensions
• On multiplicative conditionally free convolution
• Multilinear function series and transforms in free probability theory