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Power series with positive coefficients arising from the characteristic polynomials of positive matrices

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Abstract

Let A be an \(n \times n\) (entrywise) positive matrix and let \(f(t)=\det (I-t A)\). We prove the surprising result that there always exists a positive integer N such that the formal power series expansion of \(1-f(t)^{1/N}\) around \(t=0\) has positive coefficients.

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Authors and Affiliations

  1. School of Mathematical Sciences, University College Dublin, Dublin 4, Ireland

    Thomas J. Laffey & Helena Šmigoc

  2. Department of Mathematics, Technion, 32000, Haifa, Israel

    Raphael Loewy

Authors
  1. Thomas J. Laffey
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  2. Raphael Loewy
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  3. Helena Šmigoc
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Corresponding author

Correspondence to Helena Šmigoc.

Additional information

This work was supported by Science Foundation Ireland under Grant 11/RFP.1/MTH/3157.

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Laffey, T.J., Loewy, R. & Šmigoc, H. Power series with positive coefficients arising from the characteristic polynomials of positive matrices. Math. Ann. 364, 687–707 (2016). https://doi.org/10.1007/s00208-015-1233-9

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