منابع مشابه
A sharpening of Fisher's inequality
Frankl, P. and Z. Filredi, A sharpening of Fisher’s inequality, Discrete Mathematics 90 (1991) 103-107. It is proved that in every linear space on v points and b lines the number of intersecting line-pairs is at least (z). This clearly implies b 2 v.
متن کاملSharpening the LYM inequality
More detailed information about the s t ructure of Sperner families can be obtained by considering their level sequences. The level sequence of a family 4 , f ( ~ ) = {fi(Y)}, has f i (~) equal to the number of members of ~ with exac t ly ' / e l emen t s . Sperner 's theorem asserts tha t ~fi(2~)<_ ([~j) . A stronger restriction on the level i sequence was proved independent ly by Lubell, Yama...
متن کاملA quantitative sharpening of Moriwaki’s arithmetic Bogomolov inequality
A. Moriwaki proved the following arithmetic analogue of the Bogomolov unstability theorem. If a torsion-free hermitian coherent sheaf on an arithmetic surface has negative discriminant then it admits an arithmetically destabilising subsheaf. In the geometric situation it is known that such a subsheaf can be found subject to an additional numerical constraint and here we prove the arithmetic ana...
متن کاملA New Sharpening of the Erdös-mordell Inequality and Related Inequalities
The famous Erdös-Mordell inequality in geometric inequalities states the following: Let P be an interior point of a triangle ABC. Let R1, R2, R3 be the distances from P to the vertices A,B,C, and let r1, r2, r3 be the distance from P to the sides BC,CA,AB, respectively. Then R1 +R2 +R3 ≥ 2(r1 + r2 + r3), (1.1) with equality if and only if △ABC is equilateral and P is its center. This equality w...
متن کاملA Slight Sharpening of LMN
Linial, Mansour and Nisan [7] proved that a function computed by a small-depth circuit of limited size has most of its Fourier support on small sets. We improve their bounds. When the bottom fanin is bounded we use essentially their argument, but to reduce the general case to this case without a loss in the asymptotic bounds requires a new argument. Warning: Essentially this paper is accepted f...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1991
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90101-7