International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 34684, 16 pages

Free dendriform algebras. Part I. A parenthesis setting

Philippe Leroux

Institut für Mathematik und Informatik, Ernst-Moritz-Arndt-Universität, Jahnstraße 15a, Greifswald 17487, Germany

Received 25 September 2005; Revised 18 September 2006; Accepted 21 September 2006

Copyright © 2006 Philippe Leroux. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose both a reformulation of some known results on the free dendriform algebra on one generator from a parenthesis setting instead of using permutations and some developments as well. Moreover, by introducing the concept of NCP-operad, we show how to use the free dendriform algebra on one generator to reformulate some results obtained by Speicher in free probability.