Three variable Boole - Mobius transform

Insights into Mathematics

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We extend our understanding of the Boole - Mobius transform from a Boolean function to a Boole polynumber, now to the case of three variables. The correspondence between the numbers from 0 to 7 , counting in binary, and subsets of our three element variable set is a crucial ingredient.

After some careful bookkeeping, a remarkable 8 x8 matrix appears which we call T_3. Its inverse is particularly interesting!