We approximate the number of linear extensions of an ordered set by counting "critical" suborders.
Inequalities for the number of linear extensions
β Scribed by A. Sidorenko
- Publisher
- Springer Netherlands
- Year
- 1992
- Tongue
- English
- Weight
- 490 KB
- Volume
- 8
- Category
- Article
- ISSN
- 0167-8094
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π 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.
Let P be a two-dimensional order, and P any complement of P, i.e., any partial order whose comparability graph is the complement of the comparability graph of P. Let e(Q) denote the number of linear extensions of the partial order Q. Sidorenko [13] showed that e(P)e(P) β₯ n!, for any two-dimensional