A New Construction for Cancellative Families of Sets
نویسندگان
چکیده
منابع مشابه
A 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 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 of Non-Extendable Intersecting Families of Sets
In 1975, Lovász conjectured that any maximal intersecting family of k-sets has at most b(e− 1)k!c blocks, where e is the base of the natural logarithm. This conjecture was disproved in 1996 by Frankl and his co-authors. In this short note, we reprove the result of Frankl et al. using a vastly simplified construction of maximal intersecting families with many blocks. This construction yields a m...
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 کاملA New Construction of Wavelet Sets
We show that the class of (dyadic) wavelet sets is in one-to-one correspondence to a special class of Lebesgue measurable isomorphisms of [0, 1) which we call wavelet induced maps. We then define two natural classes of maps WI1 and WI2 which, in order to simplify their construction, retain only part of the characterization properties of a wavelet induced map. We prove that each wavelet induced ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 1996
ISSN: 1077-8926
DOI: 10.37236/1239