Template:Gender of Boolean functions/triangles/male



This triangle shows the numbers of male Boolean functions with arity $$n$$ and valency $$k$$. The right diagonal is $$\boldsymbol{q}(n) = 2 ^ {(2 ^ n - 1)}$$. (That is half the number of all $$n$$-ary Boolean functions.)  (like, but with offset 0) This is Pascal's triangle with column $$k$$ multiplied by $$\boldsymbol{q}(k)$$.

The row sums are.

These images show the male functions also seen in the two 8×256 matrices. (Only a few of the 128 on the right side of the matrix are shown.) They are ordered by adicity (vertical) and valency (horizontal). The numbers sum up to those in the triangle above. (E.g. 2 + 2 + 2 = 6 and 8 + 16 = 24.)