Abstract

In this paper, we introduce description trees, to give a general framework for the recursive decompositions of several families of planar maps studied by W.T. Tutte. These trees reflect the combinatorial structure of the decompositions and carry out various combinatorial parameters. We also introduce left regular trees as canonical representants of some new conjugacy classes on planted plane trees. We give an enumeration formula for these trees. In several cases the combination of these two ingredients yields a purely combinatorial proof of some elegant formulae of W.T. Tutte and gives uniform random generation algorithms for the corresponding planar maps. Rsum Dans cet article, nous introduisons des arbres de description pour coder la dcomposition rcursive de plusieurs familles de cartes planaires tudies par W.T. Tutte. Ces arbres refltent la structure combinatoire de la dcomposition et portent diffrents paramtres combinatoires. Nous introduisons aussi les arbres rguliers gauches qu...

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