Falsity of Wangʹs conjecture on stars Original Research Article

Let Ωn denote the set of all n × n doubly stochastic matrices. E.T.H. Wang called a matrix B ε Ωn a star if per (αB + (1 − α)A) less-than-or-equals, slant αper(B) + (1 − α) per(A) for all A ε Ωn and for all α ε [0, 1] and conjectured in 1979 that for n greater-or-equal, slanted 3, permutation matrices are the only stars. In this paper we disprove Wangʹs conjecture for n = 3, by showing that PBQ is a star where image and P and Q are permutation matrices. We also establish that the only stars in Ω3 are PBQ as defined above.