a separable permutation is a permutation that can be obtained from the trivial permutation 1 by direct sums and skew sums. Separable permutations may...

independent variables Separable permutation, a permutation that can be obtained by direct sums and skew sums of the trivial permutation Separable polynomial, a...

theoretical computer science, a (classical) permutation pattern is a sub-permutation of a longer permutation. Any permutation may be written in one-line notation...

Josephus permutation Parity of a permutation Separable permutation Stirling permutation Superpattern Transposition (mathematics) Unpredictable permutation Bijection...

mathematics and computer science, a stack-sortable permutation (also called a tree permutation) is a permutation whose elements may be sorted by an algorithm...

In mathematics, a polynomial P(X) over a given field K is separable if its roots are distinct in an algebraic closure of K, that is, the number of distinct...

pattern 312. Like the stack-sortable permutations, they are also a subset of the separable permutations, the permutations formed by recursive combinations...

square if and only if the inactive cells have the pattern of a separable permutation. In any higher dimension, for any threshold, there is an analogous...

graph of a series-parallel partial order. A cograph is a permutation graph of a separable permutation. A cograph is a graph all of whose minimal chordal completions...

equations that are solvable by radicals in terms of properties of the permutation group of their roots—an equation is by definition solvable by radicals...

called separable permutations; they arise in the study of sortability theory, and can also be characterized as permutations avoiding the permutation patterns...

has a realizer in which one of the two permutations is the identity and the other is a separable permutation. It is known that a partial order P has...

fully separable states and fully entangled states, there also exists the notion of partially separable states. The definitions of fully separable and fully...

cuts: The Schröder number S n {\displaystyle S_{n}} also counts the separable permutations of length n − 1. {\displaystyle n-1.} Schröder numbers are sometimes...

In mathematics, there are up to isomorphism exactly two separably acting hyperfinite type II factors; one infinite and one finite. Murray and von Neumann...

a discipline within the field of abstract algebra, a resolvent for a permutation group G is a polynomial whose coefficients depend polynomially on the...

the idea was first noticed, is that of finite groups (see primitive permutation group). Consider a group G and subgroups H and K, with K contained in...

can be switched with any other, either by a permutation that swaps just those two atoms, or by a permutation that swaps the two carbons and each hydrogen...

them. For a more elementary discussion of Galois groups in terms of permutation groups, see the article on Galois theory. Suppose that E {\displaystyle...

Algebraically closed field Algebraic element Algebraic closure Separable extension Separable polynomial Normal extension Galois extension Abelian extension...

sequence and its permutation. The complement of a permutation graph is another permutation graph, for the reverse of the given permutation. Therefore, as...

through a 5→4 bit S-box. Mix adjacent 4-bit blocks using a maximum distance separable code over GF(24). Permute 4-bit blocks so that they will be adjacent to...

lead to calculating all permutations of gene pairs for each individual or row. Given the formula for calculating the permutations of n items with a group...

mechanical systems A {\displaystyle A} and B {\displaystyle B} , to be separable. It is also called the PPT criterion, for positive partial transpose....

Neumann algebra that acts on a separable Hilbert space is called separable. Note that such algebras are rarely separable in the norm topology. The von...

|j\rangle \langle i|_{B}} is the permutation or flip operator that exchanges the two subsystems A and B. Werner states are separable for p ≥ 1⁄2 and entangled...

smooth for large enough r {\displaystyle r} . In general one has to use separable closures instead of algebraic closures. If F {\displaystyle F} is a field...

arise in practice. As an example, a separable Hilbert space can only have a countable Schauder basis, but a non-separable Hilbert space may have an uncountable...

} For any p ≥ 1, the metric space (Pp(M), Wp) is separable, and is complete if (M, d) is separable and complete. It is also possible to consider the...

equivalently, Galois extension, since any subextension of a separable extension is separable) if and only if H is a normal subgroup of Gal(E/F). In this...