Szemerédi–Trotter-type theorems in dimension 3
نویسندگان
چکیده
منابع مشابه
Plünnecke and Kneser type theorems for dimension estimates
Given a division ring K containing the field k in its center and two finite subsets A and B of K∗, we give some analogues of Plünnecke and Kneser Theorems for the dimension of the k-linear span of the Minkowski product AB in terms of the dimensions of the k-linear spans of A and B. We also explain how they imply the corresponding more classical theorems for abelian groups. These Plünnecke type ...
متن کاملIntersection theorems under dimension constraints
In [8] we posed a series of extremal (set system) problems under dimension constraints. In the present paper we study one of them: the intersection problem. The geometrical formulation of our problem is as follows. Given integers 0 ≤ t, k ≤ n determine or estimate the maximum number of (0, 1)–vectors in a k–dimensional subspace of the Euclidean n–space Rn, such that the inner product (“intersec...
متن کاملProjection Theorems Using Effective Dimension
In this paper we use the theory of computing to study fractal dimensions of projections in Euclidean spaces. A fundamental result in fractal geometry is Marstrands projection theorem, which shows that for every analytic set E, for almost every line L, the Hausdorff dimension of the orthogonal projection of E onto L is maximal. We use Kolmogorov complexity to give two new results on the Hausdorf...
متن کاملParametrized Ramsey theorems in infinite dimension∗
In certain circumstances, one-dimensional parametrized Ramsey theorems extend to infinite dimension. As a consequence, countable products of many forcings do not add splitting reals.
متن کاملRamsey-type theorems for lines in 3-space
The proofs of these statements all follow from geometric incidence bounds – such as the Guth-Katz bound on pointline incidences in R – combined with Turán-type results on independent sets in sparse graphs and hypergraphs. As an intermediate step towards the third result, we also show that for a fixed family of plane algebraic curves with s degrees of freedom, every set of n points in the plane ...
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: Advances in Mathematics
سال: 2015
ISSN: 0001-8708
DOI: 10.1016/j.aim.2014.11.014