The clone of operations preserving a cycle with loops (Q1013986)
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scientific article; zbMATH DE number 5547247
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The clone of operations preserving a cycle with loops |
scientific article; zbMATH DE number 5547247 |
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The clone of operations preserving a cycle with loops (English)
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24 April 2009
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The paper deals with clones that are polymorphism classes of all the binary relations on a \(k\)-element set consisting of a \(k\)-cycle and some loops (viewed as a directed graph). The main result states that if \(k\geq 3\) and the considered relation has at least two loops, then it is only preserved by essentially unary operations. In all other cases, the relations are preserved by operations that depend on a greater number of variables.
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clone
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permutation
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essentially unary operation
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collapsing monoid
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