A short proof of a cross-intersection theorem of Hilton
نویسنده
چکیده
Families A1, ...,Ak of sets are said to be cross-intersecting if Ai ∩ Aj 6= ∅ for any Ai ∈ Ai and Aj ∈ Aj , i 6= j. A nice result of Hilton that generalises the Erd®sKo-Rado (EKR) Theorem says that if r ≤ n/2 and A1, ..., Ak are cross-intersecting sub-families of ( [n] r ) , then
منابع مشابه
A SHORT PROOF FOR THE EXISTENCE OF HAAR MEASURE ON COMMUTATIVE HYPERGROUPS
In this short note, we have given a short proof for the existence of the Haar measure on commutative locally compact hypergroups based on functional analysis methods by using Markov-Kakutani fixed point theorem.
متن کاملGroups with one conjugacy class of non-normal subgroups - a short proof
For a finite group $G$ let $nu(G)$ denote the number of conjugacy classes of non-normal subgroups of $G$. We give a short proof of a theorem of Brandl, which classifies finite groups with $nu(G)=1$.
متن کاملOn the norm of the derived subgroups of all subgroups of a finite group
In this paper, we give a complete proof of Theorem 4.1(ii) and a new elementary proof of Theorem 4.1(i) in [Li and Shen, On the intersection of the normalizers of the derived subgroups of all subgroups of a finite group, J. Algebra, 323 (2010) 1349--1357]. In addition, we also give a generalization of Baer's Theorem.
متن کاملA new proof for the Banach-Zarecki theorem: A light on integrability and continuity
To demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the Banach-Zareckitheorem is presented on the basis of the Radon-Nikodym theoremwhich emphasizes on measure-type properties of the Lebesgueintegral. The Banach-Zarecki theorem says that a real-valuedfunction $F$ is absolutely continuous on a finite closed intervalif and only if it is continuo...
متن کاملExtension of Krull's intersection theorem for fuzzy module
In this article we introduce $mu$-filtered fuzzy module with a family of fuzzy submodules. It shows the relation between $mu$-filtered fuzzy modules and crisp filtered modules by level sets. We investigate fuzzy topology on the $mu$-filtered fuzzy module and apply that to introduce fuzzy completion. Finally we extend Krull's intersection theorem of fuzzy ideals by using concept $mu$-adic comp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete Mathematics
دوره 309 شماره
صفحات -
تاریخ انتشار 2009