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Exponent Profiles of Oscillatory Matrices under Matrix and Inverse Sparsity
We classify the simultaneous half-bandwidths \(p,q\) of a symmetric oscillatory matrix \(A\) and its inverse. At order \(n\ge2\), the possible pairs are \((1,n-1)\), \((n-1,1)\), and all pairs with \(2\le p,q\le n-1\). Every pair has an integer realization of determinant one. Let \(e_k(A)\) be the
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