Graph polynomials serve as robust algebraic encodings of the intricate combinatorial properties inherent to graphs. At the heart of this discipline lies the Tutte polynomial, an invariant that not ...

The theory of Appell polynomials has long intrigued researchers due to its elegant algebraic structure and rich connections with differential equations. At its core, an Appell sequence is ...

How many times during your educational career have you thought to yourself, “When on earth am I ever -- and I mean ever -- going to use this?” I would venture to guess we’ve all thought this a time or ...

Equations, like numbers, cannot always be split into simpler elements. Researchers have now proved that such “prime” equations become ubiquitous as equations grow larger. Prime numbers get all the ...

Vesselin Dimitrov’s proof of the Schinzel-Zassenhaus conjecture quantifies the way special values of polynomials push each other apart. In the physical world, objects often push each other apart in an ...

Illustration of a set of real zeros of a graph polynomial (middle) and two Feynman diagrams. Credit: Max Planck Institute for Mathematics in the Sciences How can the behavior of elementary particles ...