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Optimal linear extensions by interchanging chains


Author: Ivan Rival
Journal: Proc. Amer. Math. Soc. 89 (1983), 387-394
MSC: Primary 06A10; Secondary 06A05, 90B35
DOI: https://doi.org/10.1090/S0002-9939-1983-0715851-3
MathSciNet review: 715851
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Abstract: For a finite ordered set $ P$ how can a linear extension $ L = {C_1} \oplus {C_2}$ be constructed which minimizes the number $ m$ of chains $ {C_i}$ of $ P$? While this question remains largely unanswered we show that a natural "greedy" algorithm is actually optimal for a far wider class of ordered sets than was hitherto suspected.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0715851-3
Keywords: Linear extension, chain decomposition
Article copyright: © Copyright 1983 American Mathematical Society

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