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- W4238047658 abstract "The automorphism group $operatorname {Aut}({Sigma _2})$ of the full $2$-shift is conjectured to be generated by the shift and involutions. We approach this problem by studying a certain family of automorphisms whose order was unknown, but which we show to be finite and for which we find factorizations as products of involutions. The result of this investigation is the explicit construction of a subgroup $mathcal {H}$ of $operatorname {Aut}({Sigma _2})$ ; $mathcal {H}$ is generated by certain involutions ${g_n}$, and turns out to have a number of curious properties. For example, ${g_n}$ and ${g_k}$ commute unless $n$ and $k$ are consecutive integers, the order of ${g_{n + k}} circ cdots circ {g_k}$ is independent of $k$, and $mathcal {H}$ contains elements of all orders. The investigation is aided by the development of results about certain new types of arrays of $0$âs and $1$âs called periodic seeded arrays, as well as the use of Boyle and Kriegerâs work on return numbers and periodic points." @default.
- W4238047658 created "2022-05-12" @default.
- W4238047658 creator A5058637443 @default.
- W4238047658 date "1993-09-01" @default.
- W4238047658 modified "2023-09-26" @default.
- W4238047658 title "Periodic Seeded Arrays and Automorphisms of the Shift" @default.
- W4238047658 doi "https://doi.org/10.2307/2154212" @default.
- W4238047658 hasPublicationYear "1993" @default.
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