Monomial Inequalities for Newton Coefficients and Determinantal Inequalities for p-Newton Matrices

  1. Johnson, C. R.
  2. Marijuán, C.
  3. Pisonero, M.
  4. Walch, O.
Buch:
Notions of Positivity and the Geometry of Polynomials

ISBN: 9783034801416,  9783034801423

Datum der Publikation: 2011

Seiten: 275-282

Art: Buch-Kapitel

DOI: 10.1007/978-3-0348-0142-3_15 GOOGLE SCHOLAR lock_openOpen Access editor

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Zusammenfassung

We consider Newton matrices for which the Newton coefficients are positive. We show that one monomial in these coefficients dominates another for all such Newton matrices if and only if a certain generalized form of majorization occurs. As the Newton coefficients may be viewed as average values of principal minors of a given size, these monomial inequalities may be interpreted as determinantal inequalities in such familiar classes as the positive definite, totally positive, and M-matrices, etc.

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