Configuration polynomials under contact equivalence
Annales de l’Institut Henri Poincaré D, Tome 9 (2022) no. 4, pp. 793-812.
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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 $$, 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.

Accepté le :
Publié le :
DOI : 10.4171/aihpd/154
Classification : 14-XX, 05-XX, 81-XX
Mots-clés : configuration, matroid, contact equivalence, Feynman, Kirchhoff, Symanzik 
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     title = {Configuration polynomials under contact equivalence},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {793--812},
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Denham, Graham; Pol, Delphine; Schulze, Mathias; Walther, Uli. Configuration polynomials under contact equivalence. Annales de l’Institut Henri Poincaré D, Tome 9 (2022) no. 4, pp. 793-812. doi : 10.4171/aihpd/154. http://archive.numdam.org/articles/10.4171/aihpd/154/

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