منابع مشابه
On Cancellative Set Families
A family of subsets of an n-set is 2-cancellative if for every four-tuple {A, B, C, D} of its members A ∪B ∪C = A ∪B ∪D implies C = D. This generalizes the concept of cancellative set families, defined by the property that A ∪B 6= A ∪C for A, B, C all different. The asymptotics of the maximum size of cancellative families of subsets of an n-set is known, (Tolhuizen [7]). We provide a new upper ...
متن کاملCancellative pairs of families of sets
A pair (~, ~) of families of subsets of an n-element set X is cancellative if, for all A, A' e .~ and B, B' E ~, the following conditions hold: A\B = A ' \ B ~ A =A' and BkA =B'kA~B = B'. We prove that every such pair satisfies I.~11~1 < 0 ~, where 0 ~2.3264. This is related to a conjecture of ErdSs and Katona on cancellative families and to a conjecture of Simonyi on recovering pairs. For the ...
متن کاملA New Construction for Cancellative Families of Sets
Following [2], we say a family, H , of subsets of a n-element set is cancellative if A∪B = A∪C implies B = C when A,B,C ∈ H . We show how to construct cancellative families of sets with c2 elements. This improves the previous best bound c2 and falsifies conjectures of Erdös and Katona [3] and Bollobas [1]. AMS Subject Classification. 05C65 We will look at families of subsets of a n-set with the...
متن کاملOn Weakly Cancellative Fuzzy Logics
Starting from a decomposition result of MTL-chains as ordinal sums, we focus our attention on a particular kind of indecomposable semihoops, namely weakly cancellative semihoops. Weak cancellation property is proved to be the difference between cancellation and pseudocomplementation, so it gives a new axiomatization of Product logic and ΠMTL. By adding this property, some new fuzzy logics (prop...
متن کاملOn Cross-Intersecting Families of Set Partitions
Let B(n) denote the collection of all set partitions of [n]. Suppose A1,A2 ⊆ B(n) are cross-intersecting i.e. for all A1 ∈ A1 and A2 ∈ A2, we have A1 ∩A2 6= ∅. It is proved that for sufficiently large n,
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ژورنال
عنوان ژورنال: Combinatorics, Probability and Computing
سال: 2007
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s0963548307008413