منابع مشابه
Cancellative 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 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 کاملComparable pairs in families of sets
Given a family F of subsets of [n], we say two sets A,B ∈ F are comparable if A ⊂ B or B ⊂ A. Sperner’s celebrated theorem gives the size of the largest family without any comparable pairs. This result was later generalised by Kleitman, who gave the minimum number of comparable pairs appearing in families of a given size. In this paper we study a complementary problem posed by Erdős and Daykin ...
متن کاملDegrees of M-fuzzy families of independent L-fuzzy sets
The present paper studies fuzzy matroids in view of degree. First wegeneralize the notion of $(L,M)$-fuzzy independent structure byintroducing the degree of $M$-fuzzy family of independent $L$-fuzzysets with respect to a mapping from $L^X$ to $M$. Such kind ofdegrees is proved to satisfy some axioms similar to those satisfiedby $(L,M)$-fuzzy independent structure. ...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1995
ISSN: 0195-6698
DOI: 10.1016/0195-6698(95)90031-4