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The --adic Pisot conjecture for pure discrete spectrum
The $\mathcal{S}$ -adic Pisot conjecture. The tiling condition holds, and $(X_{\boldsymbol{\sigma}}, \Sigma, \mu)$ has pure discrete spectrum. This conjecture generalizes the classi…
Conjectureopenpisot-substitutions s-adic-dynamics symbolic-dynamicsarXiv posted 2 days ago
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Pure discrete spectrum implies the tiling condition for S-adic shifts
Let $\boldsymbol{\sigma} \in \mathcal{S}_d^{\mathbb{Z}}$ , with $d \ge 2$ , be a primitive sequence of unimodular substitutions that admits generalized right and left eigenvectors. S…
Conjectureopens-adic-dynamics spectral-theory symbolic-dynamicsarXiv posted 2 days ago

The --adic Pisot conjecture for pure discrete spectrum