Partitioning the Boolean lattice into copies of a poset
نویسندگان
چکیده
منابع مشابه
Incomparable Copies of a Poset in the Boolean Lattice
Let Bn be the poset generated by the subsets of [n] with the inclusion as relation and let P be a nite poset. We want to embed P into Bn as many times as possible such that the subsets in di erent copies are incomparable. The maximum number of such embeddings is asymptotically determined for all nite posets P as 1 t(P ) ( n bn/2c ) , where t(P ) denotes the minimal size of the convex hull of a ...
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Let P be a partially ordered set. If the Boolean lattice (2[n],⊂) can be partitioned into copies of P for some positive integer n, then P must satisfy the following two trivial conditions: (1) the size of P is a power of 2, (2) P has a unique maximal and minimal element. Resolving a conjecture of Lonc, it was shown by Gruslys, Leader and Tomon that these conditions are sufficient as well. In th...
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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 p...
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Let 2[n] denote the Boolean lattice of order n, that is, the poset of subsets of {1, . . . , n} ordered by inclusion. Extending our previous work on a question of Füredi, we show that for any c > 1, there exist functions e(n) ∼ √n/2 and f(n) ∼ c √ n log n and an integer N (depending only on c) such that for all n > N , there is a chain decomposition of the Boolean lattice 2[n] into ( n ⌊n/2⌋ ) ...
متن کاملPartitioning Boolean lattices into antichains
Let f(n) be the smallest integer t such that a poset obtained from a Boolean lattice with n atoms by deleting both the largest and the smallest elements can be partitioned into t antichains of the same size except for possibly one antichain of a smaller size. In this paper, it is shown that f(n)6 b n=log n. This is an improvement of the best previously known upper bound for f(n). c © 2002 Elsev...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2019
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2018.07.003