On the Monotonicity of the Number of Positive Entries in Nonnegative Four Element Matrix Powers - Brower, Cole Rubin; Ponomarenko, Vadim (The PUMP Journal of Undergraduate Research, 2020)
Let A be a nonnegative square matrix of order m and let F(A) denote the number of positive entries in A. We consider conditions on A to make the sequence F(An)n≥1 monotone. This is known for F(A) ≤ 3 and F(A) ≥ m2-2m+2; we extend this to F(A)=4.