Bases of certain finite groups
Bergman complexes, Coxeter arrangements, and graph associahedra.
Binomial residues
A binomial residue is a rational function defined by a hypergeometric integral whose kernel is singular along binomial divisors. Binomial residues provide an integral representation for rational solutions of -hypergeometric systems of Lawrence type. The space of binomial residues of a given degree, modulo those which are polynomial in some variable, has dimension equal to the Euler characteristic of the matroid associated with .
Bipartite graphs that are not circle graphs
The following result is proved: if a bipartite graph is not a circle graph, then its complement is not a circle graph. The proof uses Naji’s characterization of circle graphs by means of a linear system of equations with unknowns in .At the end of this short note I briefly recall the work of François Jaeger on circle graphs.
Broken Circuits in Matroids-Dohmen’s Inductive Proof
Dohmen [4] gives a simple inductive proof of Whitney’s famous broken circuits theorem. We generalise his inductive proof to the case of matroids