I am currently a student at the Lycée Louis-Le-Grand in Paris in Classes Préparatoires, which corresponds to the first year of University. The present paper summarizes a research project that I started at the Clay Research Academy 2005 under the supervision of Prof. Richard P. Stanley and Dr. Federico Ardila and completed after returning back from the Academy. At various stages of this work, I benefited from e-mail exchanges with Federico whom I met again at the International Mathematical Olympiad in July 2005. Back to France, numerous discussions with Xavier Caruso, a graduate student at the Ecole Normale Supérieure in Paris, contributed to improve the paper. In my spare time, I enjoy swimming and reading, especially science fiction.
Richard Stanley, Department of Mathematics, M.I.T.