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Watermelon uniform random generation with applications

✍ Scribed by Nicolas Bonichon; Mohamed Mosbah

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
427 KB
Volume
307
Category
Article
ISSN
0304-3975

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✦ Synopsis

Watermelons are particular conΓΏgurations of vicious walkers. In these conΓΏgurations, each path starts and ends at the same ordinate. We present a simple uniform random generation algorithm of watermelons based on enumeration formulas of star conΓΏgurations (with or without a wall). The performance of this algorithm is better than earlier ones in the case of watermelons with few walkers.

Using appropriate bijections, these algorithms can also generate underdiagonal paths, realizers (or Schnyder Trees), twin parallelogram polyominoes according to their perimeter and width, Baxter permutations according to the number of rises, etc. Moreover, we present some experimental results on the height of watermelons and realizers.

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Let U and V be independent random variables with continuous density function on the interval (0, 1). We describe families of functions g for which uniformity of U and V is equivalent to uniformity of g(U, V) on (0, 1). These results axe used to prescribe methods for improving the quality of pseudo-r