Multinomial identities arising from the free probability theory

Abstract

We prove a family of new identities fulfilled by multinomial coefficients, which were conjectured by Dykema and Haagerup. Our method bases on a study of the, so-called, triangular operator T by the means of the free probability theory.

20 pages; figures in PSTricks

References in corpus (1)

• Generating functions for moments of the quasi-nilpotent DT-operator

Cited by in corpus (8)

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• On algebra-valued R-diagonal elements (with erratum)
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• Some non-spectral DT-operators in finite von Neumann algebras
• Generalized Cauchy identities, trees and multidimensional Brownian motions. Part II: Combinatorial differential calculus
• Macroscale behavior of random lower triangular matrices
• Random matrices, continuous circular systems and the triangular operator