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- W2607027199 abstract "Let $mathcal Bsubseteqmathbb N$ be a primitive set. We complement results on heredity of the $mathcal B$-free subshift $X_eta$ from [arxiv:1509.08010] in two directions: In the proximal case we prove that a subshift $X_varphi$, which micht be slightly larger than the subshift $X_eta$, is always hereditary. (There is no need to assume that the set $mathcal B$ has light tails, but if $mathcal B$ does have light tails, then $X_varphi=X_eta$ [arxiv:1702.02375].) We also generalize the the concept of heredity to the non-proximal (and hence non-hereditary) case by proving that $X_varphi$ is always hereditary away from its unique minimal (which is alway Toeplitz). Finally we characterize regularity of this Toeplitz subsystem equivalently by the condition $m_H(overline{operatorname{int}(W)})=0$, where $W$ (the window) is a subset of a compact abelian group $H$ canonically associated with the set $mathcal B$, and $m_H$ denotes Haar measure on $H$. Throughout, results from [arxiv:1702.02375] are heavily used." @default.
- W2607027199 created "2017-04-28" @default.
- W2607027199 creator A5046884677 @default.
- W2607027199 date "2017-04-13" @default.
- W2607027199 modified "2023-09-27" @default.
- W2607027199 title "Generalized heredity in $mathcal B$-free systems" @default.
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