On the Number of Indecomposable Permutations with a Given Number of Cycles
نویسندگان
چکیده
Abstract. A permutation a1a2 . . . an is indecomposable if there does not exist p < n such that a1a2 . . . ap is a permutation of {1, 2, . . . , p}. We consider the probability that a permutation of Sn with m cycles is indecomposable and prove that this probability is monotone non-increasing in n. We compute also the asymptotic probability when n goes to infinity with m/n tending to a fixed ratio. The asymptotic probability is monotone in m/n, and there is no threshold phenomenon: it degrades gracefully from 1 to 0. When n = 2m, a slight majority (51.117 . . . percent) of the permutations are indecomposable.
منابع مشابه
Indecomposable permutations with a given number of cycles
A permutation a1a2 . . . an is indecomposable if there does not exist p < n such that a1a2 . . . ap is a permutation of {1, 2, . . . , p}. We compute the asymptotic probability that a permutation of Sn with m cycles is indecomposable as n goes to infinity with m/n fixed. The error term is O( log(n−m) n−m ). The asymptotic probability is monotone in m/n, and there is no threshold phenomenon: it ...
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 19 شماره
صفحات -
تاریخ انتشار 2012