Schröder trees, antipode formulas and non-commutative probability

Adrian  Celestino; Yannic Vargas

Schröder trees, antipode formulas and non-commutative probability

Institute of Discrete Mathematics (5050)

Research output: Working paper › Preprint

Abstract

We obtain a cancellation-free formula, represented in terms of Schröder trees, for the antipode in the double tensor Hopf algebra introduced by Ebrahimi-Fard and Patras. We apply the antipode formula in the context of non-commutative probability and recover cumulant-moment formulas as well as a new expression for Anshelevich's free Wick polynomials in terms of Schröder trees.

Original language	English
Number of pages	38
Publication status	Submitted - 14 Nov 2023

Keywords

math.CO
math.PR
math.RA

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2311.07824v1Licence: Unspecified

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abstract = "We obtain a cancellation-free formula, represented in terms of Schr{\"o}der trees, for the antipode in the double tensor Hopf algebra introduced by Ebrahimi-Fard and Patras. We apply the antipode formula in the context of non-commutative probability and recover cumulant-moment formulas as well as a new expression for Anshelevich's free Wick polynomials in terms of Schr{\"o}der trees. ",

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T1 - Schröder trees, antipode formulas and non-commutative probability

AU - Celestino, Adrian

AU - Vargas, Yannic

N1 - 38 pages

PY - 2023/11/14

Y1 - 2023/11/14

N2 - We obtain a cancellation-free formula, represented in terms of Schröder trees, for the antipode in the double tensor Hopf algebra introduced by Ebrahimi-Fard and Patras. We apply the antipode formula in the context of non-commutative probability and recover cumulant-moment formulas as well as a new expression for Anshelevich's free Wick polynomials in terms of Schröder trees.

AB - We obtain a cancellation-free formula, represented in terms of Schröder trees, for the antipode in the double tensor Hopf algebra introduced by Ebrahimi-Fard and Patras. We apply the antipode formula in the context of non-commutative probability and recover cumulant-moment formulas as well as a new expression for Anshelevich's free Wick polynomials in terms of Schröder trees.

KW - math.CO

KW - math.PR

KW - math.RA

M3 - Preprint

BT - Schröder trees, antipode formulas and non-commutative probability

ER -

Schröder trees, antipode formulas and non-commutative probability

Abstract

Keywords

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