Geodesic
The face vector of a half-open hypersimplex
Journal of integer sequences, Tome 18 (2015) no. 6
The half-open hypersimplex $\Delta '_{n,k}$ consists of those $(x_{1}, \dots , x_{n}) \in $ [0,1]$^{n}$ with $k - 1 x_{1} + \dots + x_{n} \le k$, where $0 k \le n$. In this paper, we study the $f$-vector of a half-open hypersimplex and its generating functions.
Keywords: half-open hypersimplex, f -vector, generating function 
@article{JIS_2015__18_6_a6,
     author = {Hibi,  Takayuki and Li,  Nan and Ohsugi,  Hidefumi},
     title = {The face vector of a half-open hypersimplex},
     journal = {Journal of integer sequences},
     year = {2015},
     volume = {18},
     number = {6},
     zbl = {1327.05016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_6_a6/}
}
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Hibi,  Takayuki; Li,  Nan; Ohsugi,  Hidefumi. The face vector of a half-open hypersimplex. Journal of integer sequences, Tome 18 (2015) no. 6. http://geodesic.mathdoc.fr/item/JIS_2015__18_6_a6/