Length of a partially ordered set
The greatest possible length of a chain (totally ordered subset) in a partially ordered set (the length of a finite chain is one less than the number of elements). There exist infinite partially ordered sets of finite length. A partially ordered set of length zero is a trivial order.
|||R.P. Dilworth, "A decomposition theorem for partially ordered sets" Ann. of Math. , 51 (1950) pp. 161–166 Zbl 0038.02003|
|||George Grätzer, General Lattice Theory, Springer (2003) ISBN 3764369965 Zbl 1152.06300|
Length of a partially ordered set. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Length_of_a_partially_ordered_set&oldid=42244