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Tag Archives: combinatorics
What I have learned in finite geometry
On September 2nd, 2014 I wrote a blog post titled learning finite geometry, in which I described how much I have learned in my first year of PhD and more importantly, the topics that I wish to learn while I … Continue reading
Posted in Combinatorics, Finite Geometry, Incidence Geometry, Research Diary
Tagged blocking set, combinatorics, finite geometry, learning, PhD, polar spaces, unitals
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Incidence Bounds and Interlacing Eigenvalues
The Szemerédi–Trotter theorem is one of the central results in discrete geometry which gives us a (tight) bound on the number of incidences, i.e., the number of pointline pairs with the point lying on the line, between finite sets of points and lines … Continue reading
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
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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
2 Comments
A timeline of the polynomial method upto combinatorial nullstellensatz
Over the past 3040 years, the socalled polynomial method has developed into a powerful tool in combinatorics and (additive) number theory. There has been a lot of recent interest in it after Dvir’s paper on the Kakeya conjecture, where he … Continue reading
Posted in Combinatorics, Finite Geometry, Polynomial Method
Tagged combinatorics, finite fields, finite geometry, polynomials
1 Comment
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
3 Comments