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The degree of a group of permutations of a finite set is the number of elements in the set. The order of a group (of any type) is the number of elements (cardinality) in the group. By Lagrange's theorem, the order of any finite permutation group of degree n must divide n! since n-factorial is the order of the symmetric group S n.
The simplest example is the Klein four-group acting on the vertices of a square, which preserves the partition into diagonals. On the other hand, if a permutation group preserves only trivial partitions, it is transitive, except in the case of the trivial group acting on a 2-element set.
Combinations and permutations in the mathematical sense are described in several articles. Described together, in-depth: Twelvefold way; Explained separately in a more accessible way: Combination; Permutation; For meanings outside of mathematics, please see both words’ disambiguation pages: Combination (disambiguation) Permutation ...
Nguyễn Phú Trọng (Vietnamese: [ŋwiən˦ˀ˥ fu˧˦ t͡ɕawŋ͡m˧˨ʔ] ⓘ new-yen foo chong; [1] 14 April 1944 – 19 July 2024) was a Vietnamese politician and communist theorist who served as general secretary of the Communist Party of Vietnam from 2011 until his death in 2024.
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Nguyễn, Văn Khang, Bùi Chi, and Hoàng Văn Hành. (2002). Từ điển Mường-Việt (A Mường-Vietnamese dictionary). Hà Nội: Nhà Xuất Bản Văn Hoá Dân Tộc. Nguyễn Văn Tài (1982). Ngữ âm tiếng Mường qua các phương ngôn [Phonetics of the Mường language through its dialects] (Ph.D.) (in Vietnamese).
Parity of a permutation; Permanent (mathematics) Permutable prime; Permutation (music) Permutation automaton; Permutation box; Permutation matrix; Permutation polynomial; Permutoassociahedron; Permutohedron; Place-permutation action; Plain hunt; Pseudorandom permutation
In mathematics, the permutation category [1] is a category where the objects are the natural numbers, the morphisms from a natural number n to itself are the elements of the symmetric group S n {\displaystyle S_{n}} and