The clone generated by the median functions

Details The clone generated by the median functions The clone generated by the median functions

2004-01-10

arxiv.org/abs/math/0401101v1

Mathematics

Rings and Algebras

9 pages

Scientific paper

Let X be a linearly ordered set of arbitrary size (finite or infinite). Natural functions on such a set one can define using the linear order include maximum, minimum and median functions. While it is clear what the clone generated by the maximum or the minimum looks like, this is not obvious for median functions. We show that every clone on X contains either no median function or all median functions, that is, the median functions generate each other.

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