The Trifference Problem

A code C is defined to be a set of S words, where a word is a sequence of n entries. We call S the size and n the length of the code. The entries of the code can have k different values, {0, .., (k − 1)}. Define a perfect k-hash code (PHC) as a code with the property that any collection of v words in the code is different at at least one index....

Controlling the behaviour of eigenvalues: The interlacing method

This thesis uses the method of interlacing polynomials to study the behaviour of eigenvalues of a matrix after a rank-one update. Specifically, interlacing polynomials, common interlacing and interlacing families are exhaustively studied. These are excellent tools to find bounds on the eigenvalues of updated matrices by keeping track of how they...

On the domination number and cop number of Erdős–Rényi random graphs

We consider the game cops and robbers, which is a pursuit-evasion game played on a graph G. The cops and the robber take turns moving across the vertices of G, where the goal for the cops is to eventually catch the robber. Specifically, we study the cop number of G, i.e. the minimum number of cops that is needed to catch the robber on G. We...

Hyperplane covering problems