Approximating the number of linear extensions
โ Scribed by Kevin Ewacha; Ivan Rival; Nejib Zaguia
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 737 KB
- Volume
- 175
- Category
- Article
- ISSN
- 0304-3975
No coin nor oath required. For personal study only.
โฆ Synopsis
We approximate the number of linear extensions of an ordered set by counting "critical" suborders.
๐ SIMILAR VOLUMES
We find asymptotic upper and lower bounds on the number of linear extensions of the containment ordering of subsets of a finite set. These agree in their most significant non-trivial terms. A related open question is described. L > 2"((n + 1)log 2 -4 log 2m -5 + o(1 ln)).
The number of linear extensions among the orientations of a bipartite graph is maximum just if the orientation itself is bipartite, the natural one.
We consider the width Wk(n) and number Lk(n) of linear extensions of a random k-dimensional order P,Jn). We show that, for each fixed k, almost surely w&n) lies between (G/2 -C)n' -'lk and 4kn' Ilk, for some constant C, and Lk(n) lies between (e -%' -"")n and (2kn' -"k)n. The bounds given also apply