Geodesic
Viewing counting polynomials as Hilbert functions via Ehrhart theory
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010).

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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. 
@article{DMTCS_2010_special_259_a66,
     author = {Breuer, Felix and Dall, Aaron},
     title = {Viewing counting polynomials as {Hilbert} functions via {Ehrhart} theory},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)},
     year = {2010},
     doi = {10.46298/dmtcs.2871},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2871/}
}
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Breuer, Felix; Dall, Aaron. Viewing counting polynomials as Hilbert functions via Ehrhart theory. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010). doi : 10.46298/dmtcs.2871. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2871/

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