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Class of covariance matrices invariant under permutations

I am reading a paper on covariance matrix estimation, and in this paper is introduced a class of covariance matrices: \begin{equation} U(q, c_0(p),M)=\{\Sigma: \sigma_{ii}\leq M,\quad \max_j\sum_{j=1}^...
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Inequality between product of companion matrices and power of Pisot number

Let $d\geqslant 2$ be an integer and consider a convergent sequence of "companion" matrices $$A_k := \begin{pmatrix} a_{k,1} & a_{k,2} & \cdots & a_{k,d} \\\ & ...
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