On a conjecture about the eigenvalues of doubly stochastic matrices - Mashreghi, Javad; Rivard, Roland (Linear & multilinear algebra, 2007)
According to a long standing conjecture, the geometric location of eigenvalues of doubly stochastic matrices of order n is exactly the union of regular k-gons anchored at 1 in the unit disc for 2 ≤ k ≤ n. It is easy to verify this fact for n = 2 , 3 . But, for n ≥ 4, it has been an open question. We show that this conjecture is wrong for n = 5 .