## The Permanent and Diagonal Products on the Set of Nonnegative Matrices with Bounded Rank

**Authors:** Yair Lavi

We formulate conjectures regarding the maximum value and maximizing matrices
of the permanent and of diagonal products on the set of stochastic matrices with
bounded rank. We formulate equivalent conjectures on upper bounds for these func-
tions for nonnegative matrices based on their rank, row sums and column sums.
In particular we conjecture that the permanent of a singular nonnegative matrix is
bounded by 1/2 times the minimum of the product of its row sums and the product of
its column sums, and that the product of the elements of any diagonal of a singular
nonnegative matrix is bounded by 1/4 times the minimum of the product of its row
sums and the product of its column sums.

**Comments:** 5 Pages.

**Download:** **PDF**

### Submission history

[v1] 2018-07-28 07:02:51

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