A calculus for the random generation of labelled combinatorial structures
Theoretical Computer Science
Uniform random generation of words of rational languages
Theoretical Computer Science - Special issue: selected papers from “GASCOM '94” and the “Polyominoes and Tilings” workshops
A method for the enumeration of various classes of column-convex polygons
Discrete Mathematics
Nondecreasing Dyck paths and q-Fibonacci numbers
Discrete Mathematics
Uniform random generation of decomposable structures using floating-point arithmetic
Theoretical Computer Science - Special issue on Caen '97
Combinatorial Algorithms: For Computers and Hard Calculators
Combinatorial Algorithms: For Computers and Hard Calculators
Tirage a pile ou face de mots de Fibonacci
Discrete Mathematics
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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 algorithm for the generation of Dyck paths with decreasing valleys by coding these paths with words of a rational language. This leads to a reject algorithm for the generation of Dyck paths with increasing peaks, with less than three failures, in average.