Root polytopes, Tutte polynomials, and a duality theorem for bipartite graphs
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1602.04449.pdf
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Author(s)
Kalman, Tamas
Postnikov, Alexander
Date Issued
January 2017
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1112/PLMS.12015
