Ex(n,P) Values

The following page contains values of $$ex(n,P)$$ for certain integers $$n$$ and patterns $$P$$.

Values
If all entries in pattern $$P$$are zero, $$ex(n,P)$$ is zero.

For a $$n \times n$$ pattern $$P$$with at least one nonzero entry, $$ex(n,P) = n^2-1$$.

This is because we can completely fill in an n x n matrix with 1-entries except for a single 0 entry corresponding to one of the 1-entries in P. This matrix avoids P, but if we completely fill in the matrix, it obviously contains P.

ex(4, L1) = 14
Let L1 be the matrix:

0 1  1  0

1 0  0  1

0 1  0  0

For the lower bound, the matrix below avoids L1:

1 1  1  1

0 1  1  1

0 1  1  1

1 1  1  1

For the upper bound, note that any 4 x 4 matrix with 15 ones will contain a 3 x 4 submatrix with all ones.