منابع مشابه
Colourful and Fractional (p, q)-theorems
Let p ≥ q ≥ d+1 be positive integers and let F be a finite family of convex sets in Rd. Assume that the elements of F are coloured with p colours. A p-element subset of F is heterochromatic if it contains exactly one element of each colour. The family F has the heterochromatic (p, q)-property if in every heterochromatic p-element subset there are at least q elements that have a point in common....
متن کاملColourful transversal theorems
We prove colourful versions of three classical transversal theorems: the Katchalski-Lewis Theorem “T(3) implies T-k”, the “T(3) implies T” Theorem for well distributed sets, and the Goodmann-Pollack Transversal Theorem
متن کاملColourful Theorems and Indices of Homomorphism Complexes
We extend the colourful complete bipartite subgraph theorems of [G. Simonyi, G. Tardos, Local chromatic number, Ky Fan’s theorem, and circular colorings, Combinatorica 26 (2006), 587–626] and [G. Simonyi, G. Tardos, Colorful subgraphs of Kneser-like graphs, European J. Combin. 28 (2007), 2188–2200] to more general topological settings. We give examples showing that the hypotheses are indeed mor...
متن کاملFractional Sylvester-Gallai Theorems∗
We prove fractional analogs of the classical Sylvester-Gallai theorem. Our theorems translate local information about collinear triples in a set of points into global bounds on the dimension of the set. Specifically, we show that if for every points v in a finite set V ⊂ C, there are at least δ|V | other points u ∈ V for which the line through v, u contains a third point in V , then V resides i...
متن کاملSimilarity theorems for fractional Fourier transforms and fractional Hankel
The significance of the similarity theorem for the fractional Fourier transform is discussed, and the properties of self-similar functions considered. The concept of the fractional Hankel transform is developed for use in the analysis of diffraction and imaging in symmetrical optical systems. The particular case of Fresnel diffraction from a circular aperture is discussed and the effects of the...
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: Discrete & Computational Geometry
سال: 2013
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-013-9559-0