منابع مشابه
Tilted Sperner families
Let A be a family of subsets of an n-set such that A does not contain distinct sets A and B with |A\B| = 2|B\A|. How large canA be? Our aim in this note is to determine the maximum size of such an A. This answers a question of Kalai. We also give some related results and conjectures.
متن کاملSaturating Sperner Families
A family F ⊆ 2[n] saturates the monotone decreasing property P if F satisfies P and one cannot add any set to F such that property P is still satisfied by the resulting family. We address the problem of finding the minimum size of a family saturating the k-Sperner property and the minimum size of a family that saturates the Sperner property and that consists only of l-sets and (l + 1)-sets.
متن کاملExceptional Families and Existence Theorems for Variational Inequality Problems
This paper introduces the concept of exceptional family for nonlinear variational inequality problems. Among other things, we show that the nonexistence of an exceptional family is a sufficient condition for the existence of a solution to variational inequalities. This sufficient condition is weaker than many known solution conditions and it is also necessary for pseudomonotone variational ineq...
متن کاملSperner type theorems with excluded subposets
Let F be a family of subsets of an n-element set. Sperner’s theorem says that if there is no inclusion among the members of F then the largest family under this condition is the one containing all bn2 celement subsets. The present paper surveys certain generalizations of this theorem. The maximum size of F is to be found under the condition that a certain configuration is excluded. The configur...
متن کاملShattering-extremal set systems from Sperner families
We say that a set system F ⊆ 2 shatters a given set S ⊆ [n] if 2 = {F ∩ S : F ∈ F}. The Sauer-Shelah lemma states that in general, a set system F shatters at least |F| sets. Here we concentrate on the case of equality. A set system is called shattering-extremal if it shatters exactly |F| sets. A conjecture of Rónyai and the second author and of Litman and Moran states that if a family is shatte...
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: Journal of Combinatorial Theory, Series A
سال: 1974
ISSN: 0097-3165
DOI: 10.1016/0097-3165(74)90011-9