منابع مشابه
On the average size of sets in intersecting Sperner families
We show that the average size of subsets of [n] forming an intersecting Sperner family of cardinality not less than ( n−1 k−1 ) is at least k provided that k 6 n=2− √ n=2 + 1. The statement is not true if n=2¿ k ¿n=2−√8n+ 1=8+9=8. c © 2002 Elsevier Science B.V. All rights reserved.
متن کاملTwo-Part and k-Sperner Families: New Proofs Using Permutations
This is a paper about the beauty of the permutation method. New and shorter proofs are given for the theorem [P. L. Erdős and G. O. H. Katona, J. Combin. Theory. Ser. A, 43 (1986), pp. 58–69; S. Shahriari, Discrete Math., 162 (1996), pp. 229–238] determining all extremal two-part Sperner families and for the uniqueness of k-Sperner families of maximum size [P. Erdős, Bull. Amer. Math. Soc., 51 ...
متن کاملTilted 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 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. ...
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: 2009
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2009.02.003