Partitioning Boolean lattices into antichains
β Scribed by Muktar Elzobi; Zbigniew Lonc
- Book ID
- 108315779
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 125 KB
- Volume
- 260
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
Let 2 [n] denote the Boolean lattice of order n, that is, the poset of subsets of {1, ..., n} ordered by inclusion. Recall that 2 [n] may be partitioned into what we call the canonical symmetric chain decomposition (due to de Bruijn, Tengbergen, and Kruyswijk), or CSCD. Motivated by a question of FΓΌ
Let 2" be the ordered set obtained from the Boolean lattice 2" by deleting both the greatest and the least elements. Definef(n) to be the minimum number k such that there is a partition of 2" into k antichains of the same size except for at most one antichain of a smaller size. In the paper we exami
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