Frankl's Conjecture for Subgroup Lattices
نویسندگان
چکیده
We show that the subgroup lattice of any finite group satisfies Frankl’s UnionClosed Conjecture. We show the same for all lattices with a modular coatom, a family which includes all supersolvable and dually semimodular lattices. A common technical result used to prove both may be of some independent interest.
منابع مشابه
Frankl's Conjecture for a subclass of semimodular lattices
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متن کاملOn averaging Frankl's conjecture for large union-closed-sets
Let F be a union-closed family of subsets of an m-element set A. Let n = |F| ≥ 2 and for a ∈ A let s(a) denote the number of sets in F that contain a. Frankl’s conjecture from 1979, also known as the union-closed sets conjecture, states that there exists an element a ∈ A with n − 2s(a) ≤ 0. Strengthening a result of Gao and Yu [7] we verify the conjecture for the particular case when m ≥ 3 and ...
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Let F be a union-closed family of subsets of an m-element set A. Let n = |F| ≥ 2. For b ∈ A let w(b) denote the number of sets in F containing b minus the number of sets in F not containing b. Frankl’s conjecture from 1979, also known as the union-closed sets conjecture, states that there exists an element b ∈ A with w(b) ≥ 0. The present paper deals with the average of the w(b), computed over ...
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 24 شماره
صفحات -
تاریخ انتشار 2017