Article: On enumeration problems in Lie–Butcher theory
Author: H. Munthe-Kaas, S. Krogstad
Journal: Future Generation Computer Systems 19 (2003) 1197–1205.
Abstract: The algebraic structure underlying non-commutative Lie–Butcher series is the free Lie algebra over ordered trees. In this paper we present a characterization of this algebra in terms of balanced Lyndon words over a binary alphabet. This yields a systematic manner of enumerating terms in non-commutative Lie–Butcher series.
Remarks in hindsight: It was a strange journal to publish this work! The journal had a special issue devoted to Geometric Integration, with many interesting papers. But, I regret that we didn’t send this to a more visible Journal.
The paper establishes an explicit basis for the Free post Lie algebra in one generator, see “On Post-Lie algebras ...” for details.
1 Nov 2002