Van der Waerden Conjecture for Mixed Discriminants

Details Van der Waerden Conjecture for Mixed Discriminants Van der Waerden Conjecture for Mixed Discriminants

2004-06-21

arxiv.org/abs/math/0406420v1

Mathematics

Combinatorics

18 pages

Scientific paper

We prove that the mixed discriminant of doubly stochastic $n$-tuples of semidefinite hermitian $n \times n$ matrices is bounded below by $\frac{n!}{n^{n}}$ and that this bound is uniquely attained at the $n$-tuple $(\frac{1}{n} I,...,\frac{1}{n} I)$. This result settles a conjecture posed by R. Bapat in 1989. We consider various generalizations and applications of this result.

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