Compositions of Random Functions on a Finite Set
نویسندگان
چکیده
منابع مشابه
On Compositions of Random Functions on a Finite Set
We establish the limiting distribution of the number Tn of random functions on a set of size n which must be composed before a constant function results. In more detail, let f1, f2, . . . be independent draws from the uniform distribution over all functions from {1, . . . , n} into itself. For t = 1, 2, . . . let gt := ft ◦ · · · ◦ f2 ◦ f1 denote the composition of the first t random maps, and ...
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If we compose sufficiently many random functions on a finite set, then the composite function will be constant. We determine the number of compositions that are needed, on average. Choose random functions f1, f2, f3, . . . independently and uniformly from among the nn functions from [n] into [n]. For t > 1, let gt = ft ◦ ft−1 ◦ · · · ◦ f1 be the composition of the first t functions. Let T be th...
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Choose random functions f1, f2, f3, . . . independently and uniformly from among the nn functions from [n] into [n]. For t > 1, let gt = ft ◦ ft−1 ◦ · · · ◦ f1 be the composition of the first t functions, and let T be the smallest t for which gt is constant(i.e. gt(i) = gt(j) for all i, j). The goal of this paper is to determine the asymptotic distribution of T . We prove that, for any positive...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2002
ISSN: 1077-8926
DOI: 10.37236/1642