An Incidence Theorem in Higher Dimensions
نویسندگان
چکیده
We prove almost tight bounds on incidences between points and k-dimensional varieties of bounded degree in R. Our main tools are the Polynomial Ham Sandwich Theorem and induction on both the dimension and the number of points.
منابع مشابه
Generalizations of the Szemerédi-Trotter Theorem
In this paper, we generalize the Szemerédi-Trotter theorem, a fundamental result of incidence geometry in the plane, to flags in higher dimensions. In particular, we employ a stronger version of the polynomial cell decomposition technique, which has recently shown to be a powerful tool, to generalize the Szemerédi-Trotter Theorem to an upper bound for the number of incidences of complete flags ...
متن کاملMulti-linear maps and Taylor’s Theorem in higher dimensions
Introduction It seems that nowadays the Taylor Theorem for multiple dimensions has been given the short shrift in the typical mathematics curriculum. At least, I did not see much of it, even though the single-variable case is, of course, familiar to everybody. It is not hard to understand why, because higher-order derivatives are much more complicated in multiple dimensions than in the single-v...
متن کاملRotating Black Holes in Higher Dimensions
The properties of higher-dimensional black holes can differ significantly from those of black holes in four dimensions, since neither the uniqueness theorem, nor the staticity theorem or the topological censorship theorem generalize to higher dimensions. We first discuss black holes of Einstein-Maxwell theory and Einstein-Maxwell-Chern-Simons theory with spherical horizon topology. Here new typ...
متن کاملPerturbations of Jordan higher derivations in Banach ternary algebras : An alternative fixed point approach
Using fixed pointmethods, we investigate approximately higher ternary Jordan derivations in Banach ternaty algebras via the Cauchy functional equation$$f(lambda_{1}x+lambda_{2}y+lambda_3z)=lambda_1f(x)+lambda_2f(y)+lambda_3f(z)~.$$
متن کاملA case study in formalizing projective geometry in Coq: Desargues theorem
Formalizing geometry theorems in a proof assistant like Coq is challenging. As emphasized in the literature, the non-degeneracy conditions lead to long technical proofs. In addition, when considering higher-dimensions, the amount of incidence relations (e.g. point-line, point-plane, line-plane) induce numerous technical lemmas. In this article, we investigate formalizing projective plane geomet...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete & Computational Geometry
دوره 48 شماره
صفحات -
تاریخ انتشار 2012