Let 
be a finite partially
ordered set. A chain in 
is a set of pairwise comparable elements (i.e., a totally
ordered subset). The partial order length
of 
is the maximum cardinal
number of a chain in 
.
For a partial order, the size of the longest chain
is called the partial order length.
Chain
See also
Addition Chain, Antichain, Brauer Chain, Chain of Circles, Dilworth's Lemma, Hansen Chain, Pappus Chain, Partial Order, Partial Order Length, PathExplore with Wolfram|Alpha
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.Referenced on Wolfram|Alpha
ChainCite this as:
Weisstein, Eric W. "Chain." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Chain.html