Configuration polynomials under contact equivalence (Q2693184)

Summary: Configuration polynomials generalize the classical Kirchhoff polynomial defined by a graph. Their study sheds light on certain polynomials appearing in Feynman integrands. Contact equivalence provides a way to study the associated configuration hypersurface. In the contact equivalence class of any configuration polynomial we identify a polynomial with minimal number of variables; it is a configuration polynomial. This minimal number is bounded by \( \binom{ r + 1}{2} \), where \(r\) is the rank of the underlying matroid. We show that the number of equivalence classes is finite exactly up to rank \(3\) and list explicit normal forms for these classes.