Partitioning the Boolean Lattice into Chains of Large Minimum Size
نویسندگان
چکیده
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 Füredi, we show that there exists a function d(n) ∼ 1 2 √ n such that for any n ≥ 0, 2[n] may be partitioned into “ n ⌊n/2⌋ ”
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عنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 97 شماره
صفحات -
تاریخ انتشار 2002