# AUSTRALASIAN JOURNAL OF COMBINATORICS Volume 45 (2009), Pages 37–42 On the number of even permutations with roots

## Abstract

Let π be an even permutation on n letters which has a root, that is, there exists an even permutation ξ such that π = ξ 2. In this article the number of this kind of π is found by using generating function techniques. This is the analogue of a result for the number of all permutations with roots. 1 Introduction and statement of the result Let An be the group of all even permutations on n letters. We say that π ∈ An has a root, if there exists ξ ∈ An such that π = ξ 2. Clearly, a given π may have one or more roots, or it may have none. Let An 2 be the set of all elements of An which have at least one root, that is, An 2 = {ξ 2: ξ ∈ An}. In this article our central aim will be to fin

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