scholarly journals Weighted restriction estimates using polynomial partitioning

2017 ◽  
Vol 115 (3) ◽  
pp. 545-598 ◽  
Author(s):  
Bassam Shayya
Keyword(s):  
Polynomial Partitioning

scholarly journals Shallow Packings, Semialgebraic Set Systems, Macbeath Regions, and Polynomial Partitioning

2019 ◽  
Vol 61 (4) ◽  
pp. 756-777
Author(s):  
Kunal Dutta ◽  
Arijit Ghosh ◽  
Bruno Jartoux ◽  
Nabil H. Mustafa
Keyword(s):  
Polynomial Partitioning ◽  
Semialgebraic Set ◽  
Set Systems ◽  
Macbeath Regions

scholarly journals Unit Distances in Three Dimensions

2012 ◽  
Vol 21 (4) ◽  
pp. 597-610 ◽  
Author(s):  
HAIM KAPLAN ◽  
JIŘÍ MATOUŠEK ◽  
ZUZANA SAFERNOVÁ ◽  
MICHA SHARIR
Keyword(s):  
Three Dimensions ◽  
Polynomial Partitioning ◽  
Similar Proof ◽  
Partitioning Technique

We show that the number of unit distances determined bynpoints in ℝ3isO(n3/2), slightly improving the bound of Clarkson, Edelsbrunner, Guibas, Sharir and Welzl [5], established in 1990. The new proof uses the recently introduced polynomial partitioning technique of Guth and Katz [12]. While this paper was still in a draft stage, a similar proof of our main result was posted to the arXiv by Joshua Zahl [28].

scholarly journals Polynomial partitioning for a set of varieties

2015 ◽  
Vol 159 (3) ◽  
pp. 459-469 ◽  
Author(s):  
LARRY GUTH
Keyword(s):  
Polynomial Partitioning ◽  
Low Degree

AbstractGiven a set Γ of low-degree k-dimensional varieties in$\mathbb{R}$n, we prove that for anyD⩾ 1, there is a non-zero polynomialPof degree at mostDso that each component of$\mathbb{R}$n\Z(P) intersectsO(Dk−n|Γ|) varieties of Γ.

scholarly journals Polynomial partitioning for several sets of varieties

2016 ◽  
Vol 19 (3) ◽  
pp. 1653-1660
Author(s):  
Pavle V. M. Blagojević ◽  
Aleksandra S. Dimitrijević Blagojević ◽  
Günter M. Ziegler
Keyword(s):  
Polynomial Partitioning

scholarly journals Constructive Polynomial Partitioning for Algebraic Curves in $\mathbb{R}^3$ with Applications

2020 ◽  
Vol 49 (6) ◽  
pp. 1109-1127
Author(s):  
Boris Aronov ◽  
Esther Ezra ◽  
Joshua Zahl
Keyword(s):  
Algebraic Curves ◽  
Polynomial Partitioning
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