Some Observations on Minimal Clones

A minimal clone is an atom of the lattice of clones. We propose a new method to study minimal clones by considering the base set Ek with k elements as a finite field and by expressing each function as a polynomial over Ek. For k = 3 we present the list of all binary minimal polynomials over GF(3) derived from Cs´ak´any’s result. Then, we discuss some properties of binary minimal linear polynomials and of binary minimal monomials.

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