International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 18, Pages 34684, 16 p.
doi:10.1155/IJMMS/2006/34684
Free dendriform algebras. I: A parenthesis setting
Philippe Leroux
Institut für Mathematik und Informatik, Ernst-Moritz-Arndt-Universität, Jahnstraße 15a, Greifswald 17487, Germany
Abstract
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.