Reflection length in affine Coxeter groups.

In any Coxeter group the conjugate of elements in its Coxeter generating set are called reflections. The length of an element with respect to this expanded generating set is its reflection length. This thesis conjectures an explicit formula to compute reflection length in affine Coxeter groups and gives a proof for all groups of rank 1 and 2. Also, it provides a proof for one inequality of the formula in affine Coxeter groups of arbitrary rank.