3-ary Boolean functions; balanced families
3-ary Boolean functions 
|
In the triangle T = 
A227724 the entry T(n,k) shows the number of balanced n-ary families that contain 2k functions.
Row n=3 has the entries 0,7,0,7.
T(3,1) = 7
[edit | edit source]The seven 3-ary families that contain 21 = 2 functions:
These are linear functions (tribe E0). They correspond to the rows of a Walsh matrix, except row 0. (The corresponding box in this cube is empty.)
  |
  | |||
  |
  | |||
  |
  | |||
  | ||||
T(3,3) = 7
[edit | edit source]The seven 3-ary families that contain 23 = 8 functions:
  tribe E2 |
  tribe E3 | |||
  tribe E1 |
  tribe E2 | |||
  tribe E1 |
  tribe E2 | |||
  tribe E1 | ||||