A Non-messing-up Phenomenon for Posets
نویسنده
چکیده
We classify finite posets with a particular sorting property, generalizing a result for rectangular arrays. Each poset is covered by two sets of disjoint saturated chains such that, for any original labeling, after sorting the labels along both sets of chains, the labels of the chains in the first set remain sorted. We also characterize posets with more restrictive sorting properties.
منابع مشابه
Classification of Posets with the Non-messing-up Property for Two Sets of Chains
The so-called Non-Messing-Up Theorem is a well known sorting result for rectangular arrays of real numbers. In [4], Donald E. Knuth attributes the result to Hermann Boerner, who mentions it in a footnote in Chapter V, §5 of [1]. Later, David Gale and Richard M. Karp include the fact as an example in [3], where they prove a more general result about order preservation in sorting procedures. The ...
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