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A Non-Messing-Up Phenomenon for Posets
Bridget Eileen Tenner
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
bridget@math.mit.edu
Annals of Combinatorics 11 (1) p.101-114 March, 2007
AMS Subject Classification: 06A07, 05A05, 05C30
Abstract:
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.
Keywords: non-messing-up, partially ordered set, sorting, linear extension

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