Packing the Boolean lattice with 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...
متن کاملPacking Posets in the Boolean Lattice
We are interested in maximizing the number of pairwise unrelated copies of a poset P in the family of all subsets of [n]. For instance, Sperner showed that when P is one element, ( n bn2 c ) is the maximum number of copies of P . Griggs, Stahl, and Trotter have shown that when P is a chain on k elements, 1 2k−1 ( n bn2 c ) is asymptotically the maximum number of copies of P . We prove that for ...
متن کاملOn Poset Boolean Algebras
Let 〈P,≤〉 be a partially ordered set. We define the poset Boolean algebra of P , and denote it by F (P ). The set of generators of F (P ) is {xp : p ∈ P}, and the set of relations is {xp ·xq = xp : p ≤ q}. We say that a Boolean algebra B is well-generated, if B has a sublattice G such that G generates B and 〈G,≤G〉 is well-founded. A wellgenerated algebra is superatomic. Theorem 1 Let 〈P,≤〉 be a...
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2019
ISSN: 0024-6107,1469-7750
DOI: 10.1112/jlms.12278