On normal matrices of zeros and ones with fixed row sum (Q1307234)

Let \({\mathcal N}_n(R;k)\) denote the class of non-symmetric irreducible \(n\times n\) \((0,1)\)-normal matrices with each row sum equal to \(k\). The paper investigates the cardinality of this set, mainly for \(k=2\). In this case, the lower bound \((n-1)! \varphi(n)/2\) is obtained, where \(\varphi\) is Euler's function, and this bound becomes exact when \(n\) is an odd prime.