2 problems

A frequency square of type $(n;\lambda)$ is an $n\times n$ array in which each symbol occurs exactly $\lambda$ times in every row and every column. Two frequency squares are orthog…

Let $L$ be a frequency square of type $F(m\lambda;\lambda^m)$. A balanced diagonal conjecture asserts that if $(m-1)\lambda$ is even, then $L$ contains a balanced diagonal. The pap…