A note on Erdős matrices and Marcus\unicode{x2013}Ree inequality

Aman Kushwaha, Raghavendra Tripathi

In 1959, Marcus and Ree proved that any bistochastic matrix $A$ satisfies ${\Delta }_n(A):={\max }_{\sigma \in S_n}{\sum }_{i=1}^{n}A(i,\sigma (i))-{\sum }_{i,j=1}^{n}A(i,j{)}^2\ge 0$. Erdős asked to charac…