A polygon is an elementary (self-avoiding) cycle in the hypercubic lattice Z d taking at least one step in every dimension. A polygon on Z d is said to be convex if its length is exactly twice the sum of the side lengths of the smallest hypercube containing it. The number of d-dimensional convex pol
Asymptotic enumeration of cographs
✍ Scribed by Vlady Ravelomanana; Loÿs Thimonier
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 283 KB
- Volume
- 7
- Category
- Article
- ISSN
- 1571-0653
No coin nor oath required. For personal study only.
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## Abstract A __full graph__ on __n__ vertices, as defined by Fulkerson, is a representation of the intersection and containment relations among a system of __n__ sets. It has an undirected edge between vertices representing intersecting sets, and a directed edge from __a__ to __b__ if the correspo
In this paper we show that the number of pairwise nonisomorphic two-dimensional posets with n elements is asymptotically equivalent to =l n!. This estimate is based on a characterization, in terms of structural decomposmon, of two-d~mensmnal posets having a umque rep~\*sentation as the intersection
Analytic methods give powerful tools for obtaining asymptotic estimates in combinatorial enumeration. When they can be used, they usually provide extremely precise results. However, there are also many situations where they do not apply, and one has to use elementary or probabilistic reasoning. Prob