Long Symmetric Chains in the Boolean Lattice
نویسندگان
چکیده
منابع مشابه
Long Symmetric Chains in the Boolean Lattice
Let [n] = {1, 2, . . . , n} be a set with n elements, and let 2[n] denote the poset of all subsets of [n] ordered by inclusion. In other words, 2[n] is the Boolean lattice of order n or the n-dimensional hypercube. It is easy (for example using a symmetric chain decomposition [1, Theorem 3.1.1]) to find n disjoint skipless (saturated) symmetric chains of length n − 2, that is n disjoint chains ...
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The Boolean lattice 2[n] is the power set of [n] ordered by inclusion. A chain c0 ⊂ · · · ⊂ ck in 2[n] is rank-symmetric, if |ci|+ |ck−i| = n for i = 0, . . . , k; and it is symmetric, if |ci| = (n− k)/2 + i. We prove that there exist a bijection p : [n] → [n] and a partial ordering < on [n](>n/2) satisfying the following properties: • ⊂ is an extension of < on [n](>n/2); • if C ⊂ [n](>n/2) is ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1996
ISSN: 0097-3165
DOI: 10.1006/jcta.1996.0062