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Chain


Let P be a finite partially ordered set. A chain in P is a set of pairwise comparable elements (i.e., a totally ordered subset). The partial order length of P is the maximum cardinal number of a chain in P. For a partial order, the size of the longest chain is called the partial order length.


See also

Addition Chain, Antichain, Brauer Chain, Chain of Circles, Dilworth's Lemma, Hansen Chain, Pappus Chain, Partial Order, Partial Order Length, Path

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References

Comtet, L. Advanced Combinatorics: The Art of Finite and Infinite Expansions, rev. enl. ed. Dordrecht, Netherlands: Reidel, p. 272, 1974.Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, p. 241, 1990.

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Chain

Cite this as:

Weisstein, Eric W. "Chain." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Chain.html

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