Spanning Trees and a Conjecture of Kontsevich
Richard P. Stanley
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
rstan@math.mit.edu
Annals of Combinatorics 2 (4) p.351-363 December, 1998
AMS Subject Classification: 05E99
Abstract:
Kontsevich conjectured that the number of zeros over the field Fq of a certain polynomial QG associated with the spanning trees of a graph G is a polynomial function of q. We show the connection between this conjecture, the Matrix–Tree Theorem, and orthogonal geometry. We verify the conjecture in certain cases, such as the complete graph, and discuss some modifications and extensions.
Keywords: spanning tree, Matrix–Tree Theorem, orthogonal geometry

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