We describe new functionality in the R (R Development Core Team (2010)) package np (Hayfield and Racine (2008)) by providing a brief overview of each approach and its implementation followed by brief illustrative examples. A simple demonstration outlining how practitioners can implement their own entropy functions is also provided.

In this paper we are interesting in the enumeration of rooted labelled trees according to the relationship between the root and its sons. Let Tn;k be the family of Cayley trees on n] such that the root has exactly k smaller sons. In a rst time we give a bijective proof of the fact that jTn+1;kj = ? n k n n?k. Moreover, we use the family Tn+1;0 of Cayley trees for which the root is smaller than ...