Root polytopes, Tutte polynomials, and a duality theorem for bipartite graphs
Author(s)Kalman, Tamas; Postnikov, Alexander
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Let G be a connected bipartite graph with colour classes E and V and root polytope Q. Regarding the hypergraph H=(V,E) induced by G, we prove that the interior polynomial of H is equivalent to the Ehrhart polynomial of Q, which in turn is equivalent to the h-vector of any triangulation of Q. It follows that the interior polynomials of H and its transpose H=(E,V) agree. When G is a complete bipartite graph, our result recovers a well-known hypergeometric identity due to Saalschütz. It also implies that certain extremal coefficients in the Homfly polynomial of a special alternating link can be read off of an associated Floer homology group.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Proceedings of the London Mathematical Society
Oxford University Press (OUP)
Kálmán, Tamás and Alexander Postnikov. “Root Polytopes, Tutte Polynomials, and a Duality Theorem for Bipartite Graphs.” Proceedings of the London Mathematical Society 114, 3 (January 2017): 561–588 © 2017 London Mathematical Society