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Tag Archives: AlonFuredi
A coding theoretic application of the AlonFüredi theorem
The AlonFüredi theorem is something that I have written a lot about in this blog. I spent a considerable amount of time on this theorem during my PhD. In fact, it’s generalisation that I obtained and it’s applications in finite … Continue reading
Covering the binary hypercube
A finite grid is a set , where is a field and each is a finite subset of . The minimum number of hyperplanes required to cover can easily be shown to be , with the hyperplanes defined by , … Continue reading
The footprint bound
Studying the set of common zeros of systems of polynomial equations is a fundamental problem in algebra and geometry. In this post we will look at estimating the cardinality of the set of common zeros, when we already know that … Continue reading
Applications of AlonFuredi to finite geometry
In a previous post I discussed how the AlonFuredi theorem serves as a common generalisation of the results of Schwartz, DeMillo, Lipton and Zippel. Here I will show some nice applications of this theorem to finite geometry (reference: Section 6 of my … Continue reading
Posted in Combinatorics, Finite Geometry, Polynomial Method
Tagged AlonFuredi, blocking set, polynomials
1 Comment
The ErdősGinzburgZiv theorem
Let be a sequence of integers (not necessarily distinct). Then there exists a subsequence of the sum of whose elements is divisible by . This is one of the first problems I saw when learning the pigeonhole principle. And it’s … Continue reading
Posted in Combinatorics, Polynomial Method
Tagged additivecombinatorics, AlonFuredi, combinatorics, polynomials
8 Comments
AlonFuredi, SchwartzZippel, DeMilloLipton and their common generalization
In the post Balls in Bins I wrote about a combinatorial function which denotes the minimum value of the product among all distributions of balls (so ) in bins with the constraints . It turns out that this combinatorial function is linked … Continue reading
Posted in Combinatorics, Polynomial Method
Tagged AlonFuredi, combinatorics, finite fields, polynomials
4 Comments
On Zeros of a Polynomial in a Finite Grid: the AlonFuredi bound
My joint paper with Aditya Potukuchi, Pete L. Clark and John R. Schmitt is now up on arXiv: arXiv:1508.06020. This work started a few months back when I emailed Pete and John, pointing out an easy generalization of ChevalleyWarning theorem using something known as … Continue reading
Posted in Combinatorics, Finite Geometry, Polynomial Method
Tagged AlonFuredi, combinatorics, finite fields, polynomials
5 Comments