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- W2977819881 abstract "Gao, Jackson, and Seward [12] proved that every countably infinite group $Gamma$ admits a nonempty free subshift $X subseteq 2^Gamma$. Here we strengthen this result by showing that free subshifts can be large in various senses. Specifically, we prove that for any $k geq 2$ and $h < log_2 k$, there exists a free subshift $X subseteq k^Gamma$ of Hausdorff dimension and, if $Gamma$ is sofic, entropy at least $h$, answering two questions attributed by Gao, Jackson, and Seward to Juan Souto [13]. Furthermore, we establish a general lower bound on the largest size of a free subshift $X'$ contained inside a given subshift $X$. A central role in our arguments is played the Lovász Local Lemma, an important tool in probabilistic combinatorics, whose relevance to the problem of finding free subshifts was first recognized by Aubrun, Barbieri, and Thomassé [3]." @default.
- W2977819881 created "2019-10-10" @default.
- W2977819881 creator A5019172041 @default.
- W2977819881 date "2019-09-30" @default.
- W2977819881 modified "2023-09-26" @default.
- W2977819881 title "Building large free subshifts using the Local Lemma" @default.
- W2977819881 doi "https://doi.org/10.4171/ggd/528" @default.
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