This thesis is divided into four parts. We present a combinatorial proof of Selberg's integral
formula, which answers a question posed by Stanley. In the second part we enumerate S …

Given any set of points $ S $ in the unit square that contains the origin, does a set of axis
aligned rectangles, one for each point in $ S $, exist, such that each of them has a point in …

When solving optimization problems that arise from real-world decision-making processes,
uncertainty is a ubiquitous phenomenon that poses a significant obstacle. More often than …

Consider a set P of points in the unit square U, one of them being the origin. For each point p
in P you may draw a rectangle in U with its lower-left corner in p. What is the maximum area …

A lower-left anchored rectangle packing of a finite set of points S (including the origin) in the
unit square is a set of axis-aligned rectangles in the unit square such that no two rectangles …