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1. Permutation group: In mathematical group theory, the set of permutations on a set of objects form a group, is called a permutation group, with composition as the group operation. For example, let A {\displaystyle A} denote a finite set of n {\displaystyle ... [100%] 2023-06-16
2. Permutation group: A permutation group is a set of permutations (cf. Permutation of a set) of a set $X$ that form a group under the operation of multiplication (composition) of permutations. (Mathematics) [100%] 2023-10-17
3. Permutation group: In mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G (which are thought of as bijective functions from the set M ... (Group whose operation is composition of permutations) [100%] 2024-06-17 [Permutation groups] [Finite groups]...
4. Permutation (music): In music, a permutation (order) of a set is any ordering of the elements of that set. A specific arrangement of a set of discrete entities, or parameters, such as pitch, dynamics, or timbre. (Music) [93%] 2023-12-13 [Permutations]
5. Permutation: In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the ... (Mathematical version of an order change) [93%] 2023-12-13 [Factorial and binomial topics] [Permutations]...
6. Permutation: of $ n $ elements A finite sequence of length $ n $ in which all the elements are different, i.e. a permutation is an arrangement of $ n $ elements without repetition. (Mathematics) [93%] 2024-01-12
7. Primitive permutation group: In mathematics, a permutation group G acting on a non-empty finite set X is called primitive if G acts transitively on X and the only partitions the G-action preserves are the trivial partitions into either a single set ... (Permutation group that preserves no non-trivial partition) [81%] 2023-04-26 [Permutation groups] [Integer sequences]...
8. Permutator: An eigen value $ \lambda $ of a stochastic kernel that it is different from one and such that $ | \lambda | = 1 $. A non-negative continuous function $ K( x, y) $ given on a compact set $ \Omega $ in a finite-dimensional space is called ... (Mathematics) [75%] 2023-01-26
9. Permeation: In physics and engineering, permeation (also called imbuing) is the penetration of a permeate (a fluid such as a liquid, gas, or vapor) through a solid. It is directly related to the concentration gradient of the permeate, a material's ... (Physics) [75%] 2023-09-30 [Physical quantities]
10. Permeation: In physics and engineering, permeation (also called imbuing) is the penetration of a permeate (a fluid such as a liquid, gas, or vapor) through a solid. It is directly related to the concentration gradient of the permeate, a material's ... (Penetration of a liquid, gas, or vapor through a solid) [75%] 2024-01-08 [Physical quantities] [Packaging]...
11. Rank 3 permutation group: In mathematical finite group theory, a rank 3 permutation group acts transitively on a set such that the stabilizer of a point has 3 orbits. The study of these groups was started by Higman (1964, 1971). [70%] 2023-03-24 [Finite groups]
12. Rank 3 permutation group: In mathematical finite group theory, a rank 3 permutation group acts transitively on a set such that the stabilizer of a point has 3 orbits. The study of these groups was started by Higman (1964, 1971). [70%] 2024-04-05 [Finite groups]
13. Primitive group of permutations: primitive permutation group A permutation group $ ( G, M) $ that preserves only the trivial equivalences on the set $ M $( i.e. equality and amorphous equivalence). (Mathematics) [66%] 2023-12-13
14. Permutation model: In mathematical set theory, a permutation model is a model of set theory with atoms (ZFA) constructed using a group of permutations of the atoms. A symmetric model is similar except that it is a model of ZF (without atoms ... (Model of set theory constructed using permutations) [66%] 2023-12-21 [Set theory]
15. Permutation relationships: permutation relations Rules for permuting the product of two creation or annihilation operators. That is, for the annihilation operators $ \{ {a( f ) } : {f \in H } \} $ and the adjoint creation operators $ \{ {a ^ \star ( f ) } : {f \in H } \} $, where $ H $ is some Hilbert ... (Mathematics) [66%] 2023-10-17
16. Pseudorandom permutation: In cryptography, a pseudorandom permutation (PRP) is a function that cannot be distinguished from a random permutation (that is, a permutation selected at random with uniform probability, from the family of all permutations on the function's domain) with practical ... (Class of functions in cryptography) [66%] 2024-01-09 [Theory of cryptography] [Cryptographic primitives]...
17. Permutation box: In cryptography, a permutation box (or P-box) is a method of bit-shuffling used to permute or transpose bits across S-boxes inputs, retaining diffusion while transposing. In block ciphers, the S-boxes and P-boxes are used to ... [66%] 2023-02-17 [Permutations]
18. Vexillary permutation: In mathematics, a vexillary permutation is a permutation μ of the positive integers containing no subpermutation isomorphic to the permutation (2143); in other words, there do not exist four numbers i < j < k < l with μ(j) < μ(i) < μ(l) < μ(k). They were ... [66%] 2022-11-19 [Permutation patterns]
19. Permutation polynomial: In mathematics, a permutation polynomial (for a given ring) is a polynomial that acts as a permutation of the elements of the ring, i.e. the map x ↦ g ( x ) {\displaystyle x\mapsto g(x)} is a bijection. [66%] 2023-01-27 [Polynomials] [Permutations]...
20. Random permutation: A random permutation is a random ordering of a set of objects, that is, a permutation-valued random variable. The use of random permutations is often fundamental to fields that use randomized algorithms such as coding theory, cryptography, and simulation. (Sequence where any order is equally likely) [66%] 2023-09-28 [Permutations] [Randomized algorithms]...