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Tag Archives: finite geometry
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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Generalized hexagons containing a subhexagon
I have recently uploaded a joint paper with Bart, “On generalized hexagons of order and containing a subhexagon”,on arXiv and submitted it for publication. In this work we extend the results of my first paper, which I discussed here, by proving the following: … Continue reading
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
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ChevalleyWarning Theorem and Blocking Sets
The classical ChevalleyWarning theorem gives us a sufficient condition for a system of polynomial equations over a finite field to have common solutions. Affine blocking sets are sets of points in an affine geometry (aka affine space) that intersect every hyperplane. … Continue reading
The Kakeya problem
The original Kakeya needle problem is to find the least amount of area required to continuously rotate a unit line segment in the (Euclidean) plane by a full rotation. Of course in a circle of diameter one we can continuously … Continue reading
Posted in Finite Geometry, Polynomial Method
Tagged combinatorics, finite fields, finite geometry
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PointLine Geometries
Some notation: The set will be denoted by . For every set we have the set of all subsets of , also known as the power set, which we will denote by . This notation makes some sense if you … Continue reading
Posted in Combinatorics, Finite Geometry
Tagged combinatorics, finite geometry, generalized quadrangles
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