Geodesic
The centers of gravity of the associahedron and of the permutahedron are the same
The electronic journal of combinatorics, Tome 17 (2010)

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In this article, we show that Loday's realization of the associahedron has the the same center of gravity as the permutahedron. This proves an observation made by F. Chapoton. We also prove that this result holds for the associahedron and the cyclohedron as realized by the first author and C. Lange.
DOI : 10.37236/344
Classification : 05E18, 05E99, 52B11, 52B12 
Christophe Hohlweg; Jonathan Lortie; Annie Raymond. The centers of gravity of the associahedron and of the permutahedron are the same. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/344
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     author = {Christophe Hohlweg and Jonathan Lortie and Annie Raymond},
     title = {The centers of gravity of the associahedron and of the permutahedron are the same},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/344},
     zbl = {1225.05246},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/344/}
}
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