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arXiv · 2005.08181

Configuration polynomials under contact equivalence

Graham Denham·Delphine Pol·Mathias Schulze·Uli Walther
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Abstract

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 $r+1\choose 2$, 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.

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Graham Denham, Delphine Pol, Mathias Schulze, Uli Walther. 2020-05-17. Configuration polynomials under contact equivalence. https://doi.org/10.4171/aihpd/154

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