COMPRESSIONS, CONVEX GEOMETRY AND THE FREIMAN–BILU THEOREM
نویسندگان
چکیده
منابع مشابه
Compressions, Convex Geometry and the Freiman-bilu Theorem
We note a link between combinatorial results of Bollobás and Leader concerning sumsets in the grid, the Brunn-Minkowski theorem and a result of Freiman and Bilu concerning the structure of sets A ⊆ Z with small doubling. Our main result is the following. If ε > 0 and if A is a finite nonempty subset of a torsion-free abelian group with |A + A| 6 K|A|, then A may be covered by e O(1) progression...
متن کاملFourier transforms and the Funk–Hecke theorem in convex geometry
We apply Fourier transforms to homogeneous extensions of functions on Sn−1. This results in complex integral operators. The real and imaginary parts of these operators provide a pairing of stereological data that leads to new results concerning the determination of convex bodies as well as new settings for known results. Applying the Funk–Hecke theorem to these operators yields stability versio...
متن کاملB -AND B - COMPLETENESS IN LOCALLY CONVEX ALGEBRAS AND THE E x THEOREM
Let E be a B-complete (B -complete) locally convex algebra and $ the topological direct sum of countably many copies of the scalar field with a jointly continuous algebra multiplication. It has been shown that E is also B-complete (B -complete) for componentwise multiplication on E . B-and Br-completeness of E , the unitization of E, and also of E x for other multiplications on E ...
متن کاملConvex and Discrete Geometry
Geir Agnarsson, Jill Bigley Dunham.* George Mason University, Fairfax, VA. Extremal coin graphs in the Euclidean plane. A coin graph is a simple geometric intersection graph where the vertices are represented by non-overlapping closed disks in the Euclidean plane and where two vertices are connected if their corresponding disks touch. The problem of determining the maximum number of edges of a ...
متن کاملConvex Geometry and Stoichiometry
We demonstrate the benefits of a convex geometric perspective for questions on chemical stoichiometry. We show that the balancing of chemical equations, the use of “mixtures” to explain multiple stoichiometry, and the half-reaction for balancing redox actions all yield nice convex geometric interpretations. We also relate some natural questions on reaction mechanisms with the enumeration of lat...
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: The Quarterly Journal of Mathematics
سال: 2006
ISSN: 1464-3847,0033-5606
DOI: 10.1093/qmath/hal009