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单词 Weak order
释义

Weak order

英语百科

Weak ordering

(重定向自Weak order)
The 13 possible strict weak orderings on a set of three elements a, b, c. The only partially ordered sets are coloured, while totally ordered ones are in black. Two orderings are shown as connected by an edge if they differ by a single dichotomy.
The permutohedron on four elements, a three-dimensional convex polyhedron. It has 24 vertices, 36 edges, and 14 two-dimensional faces, which all together with the whole three-dimensional polyhedron correspond to the 75 weak orderings on four elements.

In mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set, some of whose members may be tied with each other. Weak orders are a generalization of totally ordered sets (rankings without ties) and are in turn generalized by partially ordered sets and preorders.

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更新时间:2025/6/19 13:38:36