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