On the number of mth roots of permutations
نویسندگان
چکیده
Letm be a fixed positive integer. It is well-known that a permutation σ of {1, . . . , n}may have one, many, or nomth roots. In this article we provide an explicit expression and a generating function for the number of mth roots of σ. Let pm(n) be the probability that a random n-permutation has an mth root. We also include a proof of the fact that pm(jq) = pm(jq + 1) = · · · = pm(jq + (q − 1)), j = 0, 1, . . . , when m is a power of a prime number q.
منابع مشابه
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ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 52 شماره
صفحات -
تاریخ انتشار 2012