The Marcus–Minc Transform Inequality

We prove the Marcus–Minc conjecture: if n ≥ 2 is an integer, A is a nonnegative n × n matrix whose row and column sums equal one, and Jn has every entry 1/n, then per A ≥ per((nJn − A)/(n − 1)). We also determine all equality cases. 2020 Mathematics Subject Classification: 15A15, 05A20, 15B51.