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- W2082353306 abstract "The symmetric group S n and the alternating group A n are groups of permutations on the set {0, 1, 2, …, n - 1} whose elements can be represented as products of disjoint cycles (the representation is unique up to the order of the cycles). In this paper, we show that whenever n ≥ k ≥ 2, the collection of all k-cycles generates S n if k is even, and generates A n if k is odd. Furthermore, we algorithmically construct generating sets for these groups of smallest possible size consisting exclusively of k-cycles, thereby strengthening results in [O. Ben-Shimol, The minimal number of cyclic generators of the symmetric and alternating groups, Commun. Algebra35(10) (2007) 3034–3037]. In so doing, our results find importance in the context of theoretical computer science, where efficient generating sets play an important role." @default.
- W2082353306 created "2016-06-24" @default.
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- W2082353306 date "2012-11-14" @default.
- W2082353306 modified "2023-09-27" @default.
- W2082353306 title "ECONOMICAL GENERATING SETS FOR THE SYMMETRIC AND ALTERNATING GROUPS CONSISTING OF CYCLES OF A FIXED LENGTH" @default.
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- W2082353306 doi "https://doi.org/10.1142/s0219498812501101" @default.
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