3-ary Boolean functions; half full secs

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3-ary Boolean functions Rdrup.svg


In the triangle T = Sloane'sA227724 the entry T(n,k) shows the number of balanced (or half full) n-ary secs that contain 2^k functions.

Row n=3 has the entries 0,7,0,7.


T(3,1) = 7[edit | edit source]

The seven 3-ary secs that contain 2^1 = 2 functions:
These are linear functions (ggbec E0). They correspond to the rows of a Walsh matrix, except row 0. (The corresponding box in this cube is empty.)


Boolean functions like 1001 1001.svg
Loupe light.svg
Boolean functions like 1001 0110.svg
Loupe light.svg
Boolean functions like 1010 1010.svg
Loupe light.svg
Boolean functions like 1010 0101.svg
Loupe light.svg
Boolean functions like 1100 1100.svg
Loupe light.svg
Boolean functions like 1100 0011.svg
Loupe light.svg
Boolean functions like 1111 0000.svg
Loupe light.svg


T(3,3) = 7[edit | edit source]

The seven 3-ary secs that contain 2^3 = 8 functions:


Boolean functions like 1100 1010.svg
Loupe light.svg

ggbec E2
Boolean functions like 1110 1000.svg
Loupe light.svg

ggbec E3
Boolean functions like 1010 1001.svg
Loupe light.svg

ggbec E1
Boolean functions like 1011 1000.svg
Loupe light.svg

ggbec E2
Boolean functions like 1100 1001.svg
Loupe light.svg

ggbec E1
Boolean functions like 1110 0100.svg
Loupe light.svg

ggbec E2
Boolean functions like 1110 0001.svg
Loupe light.svg

ggbec E1