The permanent of an 
integer matrix with
all entries either 0 or 1 is 0 iff the matrix
contains an 
submatrix of 0s with 
. This result follows from the König-Egeváry
theorem.
Frobenius-König Theorem
See also
Integer Matrix, König-Egeváry Theorem, PermanentExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Frobenius-König Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Frobenius-KoenigTheorem.html