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 ...

Python allows free creation of plots, unlike expensive, stagnant graphing calculators. Import NumPy and Matplotlib for basic linear and polynomial plots in Python. Seaborn lets you make statistical ...

The second path matrix S(G) collects all the second paths in the graph G. Its characteristic polynomial shows some regularity in several particular graphs, such as paths, cycles, stars and complete ...

The quantum Bruhat graph, which is an extension of the graph formed by covering relations in the Bruhat order, is naturally related to the quantum cohomology ring of G/B. We enhance a result of Fulton ...

Combinatorial counting problems have rich connections to many areas of science including to algebra, probability, and dynamical systems in mathematics as well as to theoretical computer science and ...