Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9513242 | Discrete Mathematics | 2005 | 11 Pages |
Abstract
For a given finite poset T whose Hasse diagram is a tree and its maximal element is its root, we compare the number of those embeddings into T of a chain of a given length which contain the maximal element of T and the number of those embeddings which do not contain the maximal element of T. For a given positive integer k, we establish average depth thresholds for T beyond which there are always more embeddings of the second kind than those of the first one. We, actually, give a better than 1 upper bound for the ratio between the numbers of these embeddings that depends on the structure of T.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
MaÅgorzata Kuchta, MichaÅ Morayne, JarosÅaw Niemiec,