Mathematics – Combinatorics
Scientific paper
2008-09-12
Mathematics
Combinatorics
11 pages, 6 figures; version 2 adds missing .bbl file for bibliography
Scientific paper
A random graph order is a partial order achieved by independently sprinkling relations on a vertex set (each with probability $p$) and adding relations to satisfy the requirement of transitivity. A \textit{post} is an element in a partially ordered set which is related to every other element. Alon et al.\ \cite{Alon} proved a result for the average number of posts among the elements $\{1,2,...,n\}$ in a random graph order on $\mathbb{Z}$. We refine this result by providing an expression for the average number of posts in a random graph order on $\{1,2,...,n\}$, thereby quantifying the edge effects associated with the elements $\mathbb{Z}\backslash\{1,2,...,n\}$. Specifically, we prove that the expected number of posts in a random graph order of size $n$ is asymptotically linear in $n$ with a positive $y$-intercept. The error associated with this approximation decreases monotonically and rapidly in $n$, permitting accurate computation of the expected number of posts for any $n$ and $p$. We also prove, as a lemma, a bound on the difference between the Euler function and its partial products that may be of interest in its own right.
Bombelli Luca
Seggev Itai
Watson Sam
No associations
LandOfFree
A Computation of the Expected Number of Posts in a Finite Random Graph Order does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A Computation of the Expected Number of Posts in a Finite Random Graph Order, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Computation of the Expected Number of Posts in a Finite Random Graph Order will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-369582