Geodesic
Poset vectors and generalized permutohedra
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) (2013).

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We show that given a poset $P$ and and a subposet $Q$, the integer points obtained by restricting linear extensions of $P$ to $Q$ can be explained via integer lattice points of a generalized permutohedron. 
@article{DMTCS_2013_special_264_a3,
     author = {Croitoru, Dorian and Oh, Suho and Postnikov, Alexander},
     title = {Poset vectors and generalized permutohedra},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)},
     year = {2013},
     doi = {10.46298/dmtcs.2319},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2319/}
}
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Croitoru, Dorian; Oh, Suho; Postnikov, Alexander. Poset vectors and generalized permutohedra. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) (2013). doi : 10.46298/dmtcs.2319. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2319/

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