On the Ilmonen-Haukkanen-Merikoski Conjecture

Abstract

Let K n be the set of all n × n lower triangular (0,1)-matrices with each diagonal element equal to 1,The Ilmonen-Haukkanen-Merikoski conjecture (the IHM conjecture) states that c n is equal to the smallest eigenvalue of Y 0 Y T 0 , whereIn this paper we present a proof of this conjecture. In our proof we use an inequality for spectral radii of nonnegative matrices.