Term-rank, permanent, and rook-polynomial preservers (Q1821840)

The term-rank is the least \(x+y\) such that x rows and y columns cover all nonzero entries in a matrix. The authors show that linear transformations over any semiring preserve term-rank if and only if they are compositions of permutations of rows and columns, transpose, and entrywise multiplication by another matrix. They obtain a similar characterization of transformations preserving permanent.