A Combinatorial Approach to the Opposite Bi-Free Partial $S$-Transform

Abstract

In this paper, we present a combinatorial approach to the opposite 2-variable bi-free partial $S$-transforms where the opposite multiplication is used on the right. In addition, extensions of this partial $S$-transforms to the conditional bi-free and operator-valued bi-free settings are discussed.

References in corpus (2)

• Conditionally Bi-Free Independence for Pairs of Algebras
• Bi-Boolean independence for pairs of algebras

Cited by in corpus (1)

• On Bi-free Multiplicative Convolution