Essentially Minimal Clones of Rank 3 on a Three-Element Set
Authors:
- Hajime MachidaHMHajime Machida
- Ivo G. RosenbergIRIvo G. Rosenberg
- 1 May 2014
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- No. 0195623X,p. 97-102
Abstract
For a non-empty set A, a clone C on A is essentially minimal if C is not a minimal clone but is minimal among all clones on A containing essential functions. For a finite set A, the rank of an essentially minimal clone C on A, which is the least arity of generators of C, is no greater than |A|. We determined, in 2013, all essentially minimal clones of rank 2 on the three-element set E 3 . In this paper, we continue and determine all essentially minimal clones of rank 3 on E 3 . There are 12 essentially minimal clones of rank 3, which are divided into two conjugate classes. This completes the search of essentially minimal clones on E 3 .Keywords
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