| Abstract: | We form the random poset ??(n, p) by including each subset of n]={1,…,n} with probability p and ordering the subsets by inclusion. We investigate the length of the longest chain contained in ??(n, p). For p≥e/n we obtain the limit distribution of this random variable. For smaller p we give thresholds for the existence of chains which imply that almost surely the length of ??(n, p) is asymptotically n(log n?log log 1/p)/log 1/p. ©2000 John Wiley & Sons, Inc. Random Struct. Alg., 16, 177–194, 2000 |
