Consider the poset 6 n of partitions of an n-element set, ordered by refinement. The sizes of the various ranks within this poset are the Stirling numbers of the second kind. Let a= 1 2 &e log(2)Γ4. We prove the following upper bound for the ratio of the size of the largest antichain to the size of
On the Largest Size of an Antichain in the Bruhat Order for
β Scribed by Alessandro Conflitti, C. M. da Fonseca, Ricardo Mamede
- Book ID
- 120755343
- Publisher
- Springer Netherlands
- Year
- 2011
- Tongue
- English
- Weight
- 290 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0167-8094
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π SIMILAR VOLUMES
A short proof of the following result of Kleitman is given: the total number of sets contained in some member of an antichain of size (i) over the n-set is at least (E) + l --+ (i) for 0 < k G in. An equally short proof of Harper's isoperimetric theorem is provided as well.
## Abstract We produce in this paper an upper bound for the number of vertices existing in a clique of maximum cardinal. The proof is based in particular on the existence of a maximum cardinal clique that contains no vertex __x__ such that the neighborhood of __x__ is contained in the neighborhood