Permanental mates of doubly stochastic matrices

PERMANENTAL

MATES

207

(b) When A E fl, such that M(A) has a finite convex decomposition, must there exist B,, B,, . , . , B, E iI, such that M( B,) is convex for i = 1,2,. . . , k, and

M(A) = ; M(Bi), i=l

{A}

= M(Bi)

f~ M(Bj)

whenever

i #j?

REFERENCES 1 2 3

4

J. L. Brenner and E. T. H. Wang, Permanental pairs of doubly stochastic matrices. II, L&zrr Algebra Appl. 28:39-41 (1979). P. M. Gibson, Permanental polytopes of doubly stochastic matrices, Linear Algebra Appl. 32:87-111 (1980). S. G. Hwang, Some nontrivial permanental mates, Linear Algebra Appl. 140:89-100 (1990). E. T. H. Wang, Permanental pairs of doubly stochastic matrices, Amer. Math. Monthly

85:188-190

(1978).

Received 29 July 1991; jinal manuscript

accepted 13 November

I991