Jean-Guy Penaud

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In this paper, we illustrate a bijective proof of the enumerative formula regarding non-separable rooted planar maps N S, by means of a class L of certain ternary trees (called left trees). Our rst step consists in determining the left trees' combinatorial enumeration according to the number of their internal nodes. We then establish a bijection between the(More)
The main result of this paper is an algorithm which generates uniformly at random a Dyck path with increasing peaks, in quasi-linear time. First, we show that the ratio between the number of Dyck paths with decreasing valleys and the number of Dyck paths with increasing peaks, of a given size, tends to a constant c=2; 303727 : : : . Then, we give an(More)
A tout sommet d’un arbre binaire on associe son nornbre de S/r-ah/et-, puis on considkre une matrice dite de ramification, qui reflkte la distribution des nombres de Strahler des fils des sommets qui ont un nombre de Strahler donne. Cette notion est alors etendue a I’ensemble des arbres binaires d’une taille donnee et on montre la forme remarquable que(More)
The purpose of this note is to give a combinatorial proof of the three-term linear recurrence for Motzkin numbers. The present work is inspired by R emy’s combinatorial proof of the linear recurrence for Catalan numbers (RAIRO Inform. Theor. 19(2) (1985) 179) and the more recent proof given by Foata and Zeilberger (J. Combin. Theory Ser. A 80(2) (1997) 380)(More)
In this paper, we give a semi-algorithm to sample uniformly at random from the Fibonacci language L = + La + Lbb. It needs a uniform bit generator and the average complexity is linear. We show that we can transform this semi-algorithm to a true algorithm still with a linear complexity. Finally, we discuss a generalization to a class of regular languages. R(More)