Vol. 3, No. 5, 2009

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Compatible associative products and trees

Vladimir Dotsenko

Vol. 3 (2009), No. 5, 567–586
Abstract

We compute dimensions and characters of the components of the operad of two compatible associative products and give an explicit combinatorial construction of the corresponding free algebras in terms of planar rooted trees.

Keywords
operads, Koszul duality, compatible structures
Mathematical Subject Classification 2000
Primary: 08B20
Secondary: 18D50, 05C05
Milestones
Received: 16 September 2008
Revised: 7 February 2009
Accepted: 16 June 2009
Published: 9 November 2009
Authors
Vladimir Dotsenko
Dublin Institute for Advanced Studies
10 Burlington Road
Dublin 4
Ireland
http://www.maths.tcd.ie/~vdots