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Viewing counting polynomials as Hilbert functions via Ehrhart theory

Abstract : Steingrímsson (2001) showed that the chromatic polynomial of a graph is the Hilbert function of a relative Stanley-Reisner ideal. We approach this result from the point of view of Ehrhart theory and give a sufficient criterion for when the Ehrhart polynomial of a given relative polytopal complex is a Hilbert function in Steingrímsson's sense. We use this result to establish that the modular and integral flow and tension polynomials of a graph are Hilbert functions.
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Felix Breuer, Aaron Dall. Viewing counting polynomials as Hilbert functions via Ehrhart theory. 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010, San Francisco, United States. pp.545-556. ⟨hal-01186300⟩

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