Of Polytopes and Associahedra
نویسندگان
چکیده
λ1 + . . .+ λm = 1, then we say that y is an affine combination of y1, . . . ,ym ∈Y . If, in addition, λi ≥ 0 for 1 ≤ i ≤ m, then we say that y is a convex combination of y1, . . . ,ym ∈ Y . A convex set is any subset of Rn that is closed under the operation of taking convex combinations. In fact, it can be shown that a subset X is convex if and only if for all x0,x1 ∈ X and 0 ≤ λ ≤ 1, the point x = (1−λ)x0 + x1 also belongs to X . Intuitively, this means that any line segment between two points in X also lies in X . So, a ball is convex whereas a star-shaped figure is not.
منابع مشابه
ar X iv : m at h / 06 09 18 4 v 1 [ m at h . C O ] 6 S ep 2 00 6 FACES OF GENERALIZED PERMUTOHEDRA
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