منابع مشابه
Almost Disjoint Large Subsets of Semigroups
There are several notions of largeness in a semigroup S that originated in topological dynamics. Among these are thick , central , syndetic and piecewise syndetic. Of these, central sets are especially interesting because they are partition regular and are guaranteed to contain substantial combinatorial structure. It is known that in (N,+) any central set may be partitioned into infinitely many...
متن کاملOn Sets of Almost Disjoint Subsets of a Set
The cardinal power of a set A is denoted by IA . Two sets A,, A2 are said to e almost disjoint if IA1 U A2I < lA i l (i = 1, 2) . e call B a transversal of the disjoint non-empty sets A,, (v E M) if Bc U A,, and B intersects each A,. (v E M) in a singleton . D1 An old and well known theorem of W . SIERPINSKI is that an infinite set of po-ver m contains more than m subsets of power m which are p...
متن کاملDisjoint subsets of integers having a constant sum
We prove that for position integers n, m and k, the set {1, 2, . . . , n} of integers contains k disjoint subsets having a constant sum m if and only if 2k − 1 ≤ m ≤ n(n+ 1)/(2k).
متن کاملGenerating all subsets of a finite set with disjoint unions
If X is an n-element set, we call a family G ⊂ PX a k-generator for X if every x ⊂ X can be expressed as a union of at most k disjoint sets in G. Frein, Lévêque and Sebő [10] conjectured that for n > 2k, the smallest k-generators for X are obtained by taking a partition of X into classes of sizes as equal as possible, and taking the union of the power-sets of the classes. We prove this conjectu...
متن کاملPairs of Disjoint q-element Subsets Far from Each Other
Let n and q be given integers and X a finite set with n elements. The following theorem is proved for n > n0(q). The family of all q-element subsets of X can be partitioned into disjoint pairs (except possibly one if (n q ) is odd), so that |A1∩A2|+ |B1 ∩B2| ≤ q, |A1 ∩B2|+ |B1 ∩A2| ≤ q holds for any two such pairs {A1, B1} and {A2, B2}. This is a sharpening of a theorem in [2]. It is also shown...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1964
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1964-0163280-9