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- Title
Configuration polynomials under contact equivalence.
- Authors
Denham, Graham; Pol, Delphine; Schulze, Mathias; Walther, Uli
- 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 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.
- Subjects
POLYNOMIALS; MATHEMATICAL equivalence; HYPERSURFACES; MATROIDS; LAPLACIAN matrices
- Publication
Annales de l'Institut Henri Poincaré D, 2022, Vol 9, Issue 4, p793
- ISSN
2308-5827
- Publication type
Article
- DOI
10.4171/AIHPD/154