منابع مشابه
CD-independent subsets in distributive lattices
The notion of CD-independence is introduced as follows. A subset X of a lattice L with 0 is called CD-independent if for any x, y ∈ X , either x ≤ y or y ≤ x or x ∧ y = 0. In other words, if any two elements of X are either Comparable or Disjoint. Maximal CD-independent subsets are called CD-bases. The main result says that any two CD-bases of a finite distributive lattice L have the same numbe...
متن کاملCDW-independent subsets in distributive lattices
A subset X of a lattice L with 0 is called CDW-independent if (1) it is CDindependent, i.e., for any x, y ∈ X , either x ≤ y or y ≤ x or x ∧ y = 0 and (2) it is weakly independent, i.e., for any n ∈ N and x, y1, . . . , yn ∈ X the inequalityx ≤ y1∨· · ·∨yn implies x ≤ yi for some i. A maximal CDW-independent subset is called a CDW-basis. With combinatorial examples and motivations in the backgr...
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Let Ed(n) be the maximum number of pairs that can be selected from a set of n points in Rd such that the midpoints of these pairs are convexly independent. We show that E2(n) > Ω(n √ log n), which answers a question of Eisenbrand, Pach, Rothvoß, and Sopher (2008) on large convexly independent subsets in Minkowski sums of finite planar sets, as well as a question of Halman, Onn, and Rothblum (20...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1970
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-21-1-45-47