## Root polytopes, Tutte polynomials, and a duality theorem for bipartite graphs

##### Author(s)

Kalman, Tamas; Postnikov, Alexander
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Show full item record##### Abstract

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.

##### Date issued

2017-01##### Department

Massachusetts Institute of Technology. Department of Mathematics##### Journal

Proceedings of the London Mathematical Society

##### Publisher

Oxford University Press (OUP)

##### Citation

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

Version: Original manuscript

##### ISSN

0024-6115

1234-5678