Vol. 3, No. 6, 2009

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A rooted-trees $q$-series lifting a one-parameter family of Lie idempotents

Frédéric Chapoton

Vol. 3 (2009), No. 6, 611–636
Abstract

We define and study a series indexed by rooted trees and with coefficients in (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
Frédéric Chapoton
Institut Camille Jordan
Université Claude Bernard Lyon 1
21 Avenue Claude Bernard
69622 Villeurbanne
France
http://math.univ-lyon1.fr/~chapoton/