The work in this thesis concerns three projects at the interface of statistical mechanics and cluster integrable systems. We describe each of these in the …
We investigate two different topics in discrete mathematics: the geometry of piecewise-linear surfaces and the long-term behavior of discrete dynamical systems. A regular polygon surface …
The famous domino shuffling algorithm was invented to generate the domino tilings of the Aztec Diamond. Using the domino height function, we view the domino …
In chapter 1, we introduce the Electrical Impedance Tomography (EIT) problem, which is a non-invasive clinical diagnosis tool. Then we discuss a discrete version of …
This thesis studies three problems stemming from different areas of combinatorics. The first problem is the study of the length of the longest path in …