The \(k\)th Lower Multiexponent of Tournament Matrices

In this paper we investigate the \(k\)th lower multiexponent \(f(n,k)\) for tournament matrices.
It was proved that \(f(m,3) = 2\) if and only if \(m \geq 11\). Thus the conjecture in [2] is disproved. Further we obtain a new sufficient condition for \(f(n,k) = 1\).