On Some Tree-Indexed Series with One and Two Parameters

  • F. ChapotonEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 314)


There is a rich algebraic setting involving free pre-Lie algebras and the combinatorics of rooted trees. In this context, one can consider the analog of formal power series, called tree-indexed series. Several interesting such series are known, including one called \(\varOmega \) and its more recent one-parameter and two-parameters generalizations. This survey article explains how one can compute their coefficients using Ehrhart polynomials of lattice polytopes.


Order polytope Rooted tree Pre-Lie algebra Ehrhart polynomial q-Bernoulli number 


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Authors and Affiliations

  1. 1.Institut de Recherche Mathématique Avancée, UMR 7501, Université de Strasbourg et CNRSStrasbourgFrance

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