Commutative algebra and graph theory are two vibrant areas of mathematics that have grown increasingly interrelated. At this interface, algebraic methods are applied to study combinatorial structures, ...

A function is a rule that is applied to one set of values to give another set of values. A function can be illustrated on a graph – points are plotted as coordinates and joined by either a straight ...

Let $U$ be an open semi-algebraic subset of $\mathbf{R}^n$ and let $X$ be a closed analytic subset of $U$ which is also a semi-algebraic set (e.g., $U = \mathbf{R}^n ...

Wolfram|Alpha: The makers of Mathematica (a very powerful mathematical software package, popular amongst applied mathematicians and engineers) bring us a "google-like" mathematical search engine. In ...

Almost perfect nonlinear (APN) functions play a pivotal role in cryptography, particularly in securing symmetric key algorithms against differential attacks. Their algebraic properties, including ...

In this paper we deal with the following problems: When do the solutions of a collection of differential equations satisfy an elementary relation, that is, when is there an equation of the form R = 0 ...