Clearly and is a permutation on the finite set.
It is easy to see that (mathbf{x}^{ij}) is a permutation on k letters with exactly two cycles determined by ((i,j)).
A latin square is a matrix of size n×n with entries from the set {1,…,n}, such that each row and each column is a permutation on {1,…,n}.
A sequence space E F is said to be symmetric if (Xπ k)) ∈ E F, whenever (X k ) ∈ E F, π is a permutation on N. A sequence X = (X k ) of fuzzy numbers is said to be I-convergent if there exists a fuzzy number X0 such that for all ε > 0, the set {n ∈ N: d ― Open image in new window (X k, X 0 ) ≥ ε} ∈ I.
A sequence space X is called (i) normal (or solid) if y = ( y k ) ∈ X whenever | y k | ≤ | x k |, k ≥ 1, for some x = ( x k ) ∈ X, (ii) monotone if it contains the canonical preimages of all its stepspaces, (iii) sequence algebra if x y = ( x k y k ) ��� X whenever x = ( x k ), y = ( y k ) ∈ X, (iv) symmetric if ( x k ) ∈ X implies ( x π ( k ) ) ∈ X where π is a permutation on ℕ. .
normal (or solid) if y = ( y k ) ∈ X whenever | y k | ≤ | x k |, k ≥ 1, for some x = ( x k ) ∈ X, monotone if it contains the canonical preimages of all its stepspaces, sequence algebra if x y = ( x k y k ) ∈ X whenever x = ( x k ), y = ( y k ) ∈ X, symmetric if ( x k ) ∈ X implies ( x π ( k ) ) ∈ X where π is a permutation on ℕ.
A linear genome is a permutation on the gene set, while a circular genome can be represented in the same way under the implicit assumption that the permutation closes back on itself.
Given a graph G V,E), an automorphism is a permutation acting on the vertices.
117 One approach to test for statistical significance is a permutation test based on randomly permuting randomised assignments in the data (following the original randomisation strategy, ie, permuting T within strata Z) and re-estimating a test statistic.
