# Category Archives: Combinatorics

## Grading a class

Imagine we had a class with students and each week they hand in a sheet of homework. Now, you choose a set of of them at random and correct only those . At the end, the grade assigned to a … Continue reading

## The Fibonacci Word

Let us define by and , and extend it to a homomorphism of by . Let us note that Something very interesting is going on, each seems to be a prefix of . We will see that this is indeed … Continue reading

## Partitions and divisors

The number of partitions of a non-negative integer is, roughly speaking, the number of ways in which we can write as a sum of positive integers disregarding the order of the terms, and we denote this number by . Formally … Continue reading

## Generating a random permutation

It is well-known that any permutation of can be written as a product of transpositions, that is, of permutations of the form with , where we recall that is the permutation satisfying and for . In this post however, we … Continue reading

## Prefix-free codes

In this post we will talk about optimal prefix codes for a particular distribution, but first, a little bit of background into the topic. We will be given a message consisting of a stream of symbols which we will translate … Continue reading