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1 LIGM - Laboratoire d-Informatique Gaspard-Monge 2 UPEM - Université Paris-Est Marne-la-Vallée 3 CNRS - Centre National de la Recherche Scientifique

Abstract : We study some sequences of polynomials that appear when we consider the successive derivatives of the tree function or Lambert-s W function. We show in particular that they are related with a generalization of Cayley trees, called Greg trees. Besides the combinatorial result in itself, it is interesting to see how this is related with previous work: similar problems were considered first by Ramanujan, and more recently in the theory of completely monotonic functions and its link with probability. Also of great interest is the fact that these Greg trees were introduced as genealogical trees in a problem of textual criticism, where they had a priori no mathematical meaning.

Author: Matthieu Josuat-Vergès -



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