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|a Kalman, Tamas
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|a Massachusetts Institute of Technology. Department of Mathematics
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|a Kalman, Tamas
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|a Postnikov, Alexander
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|a Postnikov, Alexander
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|a Root polytopes, Tutte polynomials, and a duality theorem for bipartite graphs
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|b Oxford University Press (OUP),
|c 2018-05-30T18:48:50Z.
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|z Get fulltext
|u http://hdl.handle.net/1721.1/115992
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|a 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.
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|a National Science Foundation (U.S.) (Grant DMS‐1100147)
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|a National Science Foundation (U.S.) (Grant DMS‐1362336)
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|a Article
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|t Proceedings of the London Mathematical Society
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