Category:2-ary Boolean functions in tesseract matrix; principalities and dominions

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2-ary     3-ary     4-ary         principalities and dominions in hypercube matrix

Principalities are sets of 2-ary Boolean functions. Interpreted a indices of 3-ary nobles, they correspond to the factions of 3-ary nobles.

Dominions are closely related to them. The matrices on the right are the transposes of those on the left.
They are relevant, because each faction can be assigned a dominion.

Each row in the table below is denoted with a king index. (It is the index of a king among the 3-ary nobles.)
In the matrices on the left the king indices are highlighted in bold.

Each colored field in the matrices below contains not just an integer in 0...15, but also the corresponding 3-ary noble integer.
For the matrix on the left the two integers in each colored field are noble index and noble value. (E.g. 15 is the noble index of 254.)

faction
size 		king
index 		great principalities great dominions
truth
tables 		Zhegalkin
indices 		truth
tables 		Zhegalkin
indices
1 0
3 2
overview

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