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Monthly Archives: July 2012
Count Twice!
In this post we’ll look in some detail a very common and important technique in combinatorics, double counting. Let’s start with an easy example involving binomial coefficient Example 1 Prove that . There is an obvious way to prove this … Continue reading
Posted in Combinatorics
10 Comments
Introduction to finite geometry II
Given an affine plane, we can introduce points at “infinity” and join those points by a line to get a system in which there are no parallel lines and any two distinct lines determine a unique point! More formally, what … Continue reading
Posted in Finite Geometry
8 Comments
Introduction to finite geometry I
We (most of us) are familiar with the Euclidean Geometry and the (really ) axioms it is based on. Let’s consider a simpler system here called Affine plane. Affine Plane Def : An Affine plane is a triple where is … Continue reading
Posted in Finite Geometry
3 Comments