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weak transitivity - перевод на русский
![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.](https://commons.wikimedia.org/wiki/Special:FilePath/Permutohedron.svg?width=200 "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.")
математика
слабая транзитивность
![electron antineutrino]].](https://commons.wikimedia.org/wiki/Special:FilePath/Beta-minus Decay.svg?width=200 "electron antineutrino]].")
![spin]]. Note the lack of reflective symmetry between the states.](https://commons.wikimedia.org/wiki/Special:FilePath/Right left helicity.svg?width=200 "spin]]. Note the lack of reflective symmetry between the states.")
![A diagram depicting the decay routes due to the charged weak interaction and some indication of their likelihood. The intensity of the lines is given by the [[CKM parameters]].](https://commons.wikimedia.org/wiki/Special:FilePath/Weak Decay (flipped).svg?width=200 "A diagram depicting the decay routes due to the charged weak interaction and some indication of their likelihood. The intensity of the lines is given by the [[CKM parameters]].")
['wi:kintə'rækʃ(ə)n]
общая лексика
слабое взаимодействие
физика
слабое бета-распадное взаимодействие
математика
слабый порядок
Определение
Википедия
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 (strictly) partially ordered sets and preorders.
There are several common ways of formalizing weak orderings, that are different from each other but cryptomorphic (interconvertable with no loss of information): they may be axiomatized as strict weak orderings (strictly partially ordered sets in which incomparability is a transitive relation), as total preorders (transitive binary relations in which at least one of the two possible relations exists between every pair of elements), or as ordered partitions (partitions of the elements into disjoint subsets, together with a total order on the subsets). In many cases another representation called a preferential arrangement based on a utility function is also possible.
Weak orderings are counted by the ordered Bell numbers. They are used in computer science as part of partition refinement algorithms, and in the C++ Standard Library.
