Geodesic
On a special class of hyper-permutahedra
Geir Agnarsson1
1George Mason University Fairfax, Virginia, U.S.A.
The electronic journal of combinatorics, Tome 24 (2017) no. 3
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Minkowski sums of simplices in ${\mathbb{R}}^n$ form an interesting class of polytopes that seem to emerge in various situations. In this paper we discuss the Minkowski sum of the simplices $\Delta_{k-1}$ in ${\mathbb{R}}^n$ where $k$ and $n$ are fixed, their flags and some of their face lattice structure. In particular, we derive a closed formula for their exponential generating flag function. These polytopes are simple, include both the simplex $\Delta_{n-1}$ and the permutahedron $\Pi_{n-1}$, and form a Minkowski basis for more general permutahedra.
DOI : 10.37236/6652
Classification : 05A15, 52B05, 52B11
Mots-clés : polytope, permutahedron, Minkowski sum, flag polynomial, exponential flag function

Geir Agnarsson  1

1 George Mason University Fairfax, Virginia, U.S.A. 
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     title = {On a special class of hyper-permutahedra},
     journal = {The electronic journal of combinatorics},
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     number = {3},
     doi = {10.37236/6652},
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Geir Agnarsson. On a special class of hyper-permutahedra. The electronic journal of combinatorics, Tome 24 (2017) no. 3. doi: 10.37236/6652

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