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Total positivity of sums, Hadamard products and Hadamard powers: Results and counterexamples

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arxiv 1612.02210 v2 pith:P35RA7FG submitted 2016-12-07 math.AC math.CAmath.CO

Shaun Fallat , Charles R. Johnson , Alan D. Sokal This is my paper · ORCID
classification math.ACmath.CAmath.CO
keywords hadamardtotalexampleshankelmatricespositivityresultstotally
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We show that, for Hankel matrices, total nonnegativity (resp. total positivity) of order r is preserved by sum, Hadamard product, and Hadamard power with real exponent t \ge r-2. We give examples to show that our results are sharp relative to matrix size and structure (general, symmetric or Hankel). Some of these examples also resolve the Hadamard critical-exponent problem for totally positive and totally nonnegative matrices.

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  1. Superstring Amplitudes, Unitarity, and Hankel Determinants of Multiple Zeta Values

    hep-th 2019-08 conditional novelty 6.0 of 10

    Unitarity of four-particle superstring tree amplitudes implies that Hankel matrices built from low-energy coefficients are totally positive, yielding new inequalities involving multiple zeta values, including irreduci...

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