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Category Archives: Combinatorics
The Cage Problem
I recently finished my research visit to UWA where I worked with John Bamberg and Gordon Royle on some finite geometrical problems related to cages. So this seems like the right time for me to write a blog post about … Continue reading
Posted in Combinatorics, Finite Geometry
Tagged cage, finite geometry, Gordon Royle, Graph Theory, John Bamberg, Moore graphs
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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
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
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The EllenbergGijswijt bound on cap sets
Four days back Jordan Ellenberg posted the following on his blog: Briefly: it seems to me that the idea of the CrootLevPach paper I posted about yesterday can indeed be used to give a new bound on the size of subsets … Continue reading
Posted in Combinatorics, Finite Geometry, Polynomial Method
Tagged capset, Dion Gijswijt, Ernie Croot, Jordan Ellenberg, Peter Pach, Seva Lev
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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
7 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
2 Comments