The $k$th Lower Multiexponent of Tournament Matrices

Abstract

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 $m\ge 11$. Thus the conjecture in [2] is disproved. Further we obtain a new sufficient condition for $f(n,k)=1$.