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