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# Adjacent Vertices on a Permutohedron

P. Gaiha and S. K. Gupta
SIAM Journal on Applied Mathematics
Vol. 32, No. 2 (Mar., 1977), pp. 323-327
Stable URL: http://www.jstor.org/stable/2100417
Page Count: 5
The convex hull Pn of $S = \{(a_{\pi(1)}, a_{\pi(2)}, \cdots, a_{\pi(n)})\mid\pi\quad\text{is a permutation of} (1, 2, 3, \cdots, n)\},$ where a1, a2, ⋯, an are integers, is defined as a permutohedron. If $a_1 < a_2 < \cdots < a_n$, it is shown that every vertex of Pn has n - 1 adjacent vertices and a method for determining the adjacent vertices is given. The algebraic description of Pn is given by considering its facets.