The height and range of watermelons without wall ( extended abstract )
نویسنده
چکیده
We determine the weak limit of the distribution of the random variables “height” and “range” on the set of p-watermelons without wall restriction as the number of steps tends to infinity. Additionally, we provide asymptotics for the moments of the random variable “height”.
منابع مشابه
The Height and Range of Watermelons without Wall
This short note adds some results in parallel to those given in [1] on the random variable height on the set of watermelons with wall. In this paper we prove weak convergence results for the random variables “height” and “range” on the set of watermelons without wall restriction, as well as asymptotics for the moments of the random variable height. The techniques applied are quite similar to th...
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Abstract. We derive asymptotics for the moments as well as the weak limit of the height distribution of watermelons with p branches with wall. This generalises a famous result of de Bruijn, Knuth and Rice [4] on the average height of planted plane trees, and results by Fulmek [9] and Katori et al. [14] on the expected value, respectively higher moments, of the height distribution of watermelons...
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