Algebraic structure of aromatic B-series

Geir Bogfjellmo

doi:10.3934/jcd.2019010

Article Contents

2019, Volume 6, Issue 2: 199-222. Doi: 10.3934/jcd.2019010

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Algebraic structure of aromatic B-series

Geir Bogfjellmo

Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway

Received: March 31, 2019

Revised: August 31, 2019

Published: November 2019

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Abstract

Aromatic B-series are a generalization of B-series. Some of the algebraic structures on B-series can be defined analogically for aromatic B-series. This paper derives combinatorial formulas for the composition and substitution laws for aromatic B-series.

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Mathematics Subject Classification: 37C10, 41A58, 16T05.

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Table 1. The coproduct $\Delta_{\mathcal{AT}}$

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Table 2. Substitution law (1 root)

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Table 3. Substitution law (0 roots)

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