Abstract

We define and study a series indexed by rooted trees and with coefficients in Q(q). We show that it is related to a family of Lie idempotents. We prove that this series is a q-deformation of a more classical series and that some of its coefficients are Carlitz q-Bernoulli numbers.

Keywords

tree series, operads, Lie idempotents, Bernoulli–Carlitz numbers

Mathematical Subject Classification 2000

Primary: 18D50

Secondary: 17D25, 05C05

Milestones

Received: 2 September 2008
Revised: 9 July 2009
Accepted: 16 August 2009
Published: 20 November 2009

Authors