Geodesic
Ehrhart Positivity for Generalized Permutohedra
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015).

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There are few general results about the coefficients of Ehrhart polynomials. We present a conjecture about their positivity for a certain family of polytopes known as generalized permutohedra. We have verified the conjecture for small dimensions combining perturbation methods with a new valuation on the algebra of rational pointed polyhedral cones constructed by Berline and Vergne. 
@article{DMTCS_2015_special_285_a49,
     author = {Castillo, Federico and Liu, Fu},
     title = {Ehrhart {Positivity} for {Generalized} {Permutohedra}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)},
     year = {2015},
     doi = {10.46298/dmtcs.2505},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2505/}
}
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Castillo, Federico; Liu, Fu. Ehrhart Positivity for Generalized Permutohedra. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015). doi : 10.46298/dmtcs.2505. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2505/

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