Abstract
A theorem by Baker and Pixley implies that any clone on a finite set is finitely generated if it contains a near-unanimity operation. This raises the question of what arity the generating operations must have. In this paper, we solve the last open bits of this problem for the majority case by showing that 5 and 8 are the smallest integers k such that every clone with a majority operation on a 3 and 4-element set, respectively, is generated by its k-ary part.
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Presented by K. Kearnes.
The research of the second author is supported by grant RFFI 13-01-00684-a.
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Kerkhoff, S., Zhuk, D. The generation of clones with majority operations. Algebra Univers. 72, 71–80 (2014). https://doi.org/10.1007/s00012-014-0291-2
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DOI: https://doi.org/10.1007/s00012-014-0291-2