منابع مشابه
NOTE - Katona's Intersection Theorem: Four Proofs
It is known from a previous paper [3] that Katona’s Intersection Theorem follows from the Complete Intersection Theorem by Ahlswede and Khachatrian via a Comparison Lemma. It also has been proved directly in [3] by the pushing–pulling method of that paper. Here we add a third proof via a new (k,k+1)-shifting technique, whose impact will be exploared elsewhere. The fourth and last of our proofs ...
متن کاملFour Proofs of the Ballot Theorem 1
One of the great pleasures in mathematics occurs when one considers several different proofs of a single result. In fact, when one considers the myriad proofs of the Pythagorean theorem and the irrationality of √ 2 constructed over the centuries, it seems we humans can never be satisfied with just one proof. Why do we continue to devise new approaches to known results? There is something in the...
متن کاملFour proofs of Gittins' multiarmed bandit theorem
We study four proofs that the Gittins index priority rule is optimal for alternative bandit processes. These include Gittins’ original exchange argument, Weber’s prevailing charge argument, Whittle’s Lagrangian dual approach, and Bertsimas and Niño-Mora’s proof based on the achievable region approach and generalized conservation laws. We extend the achievable region proof to infinite countable ...
متن کاملAn intersection theorem for four sets
Fix integers n, r ≥ 4 and let F denote a family of r-sets of an n-element set. Suppose that for every four distinct A,B,C,D ∈ F with |A∪B ∪C ∪D| ≤ 2r, we have A∩B ∩C ∩D 6= ∅. We prove that for n sufficiently large, |F| ≤ ( n−1 r−1 ) , with equality only if ⋂ F∈F F 6= ∅. This is closely related to a problem of Katona and a result of Frankl and Füredi [10], who proved a similar statement for thre...
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...
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ژورنال
عنوان ژورنال: COMBINATORICA
سال: 2004
ISSN: 0209-9683,1439-6912
DOI: 10.1007/s00493-005-0008-4