Let A be an n by n doubly substochastic matrix and denote {\sigma}(A) the sum
of all elements of A. In this paper we give the upper bound of the permanent of
(I-A) with respect to n and {\sigma}(A)

Cao, Lei

Chen, Zhi

English

arXiv

Let ω8n and ~ω8n  denote the convex sets of  doubly substochastic matrices and row substochastic matrices with the sum of all entries equal to s, respectively. In this paper, we give the upper bound of the permanent of I - A for A ϵ ~ω8n. We also give the upper bound of the permanent of I - A for A ϵ ~ω8n, where either n is even, or n is odd and s ≤ n - 1. For the case when n is odd and n - 1 \u3c s ≤ n, we give some discussion and conjectures.
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On the maximum of the permanent of (I-A)

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