# permutation group

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## permutation group

[‚pər·myə′tā·shən ‚grüp]
(mathematics)
The group whose elements are permutations of some set of symbols where the product of two permutations is the permutation arising from successive application of the two. Also known as substitution group.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Alperin-Sheriff and Peikert  proposed an efficient bootstrapping algorithm by embedding [Z.sub.q] into permutation group Sq.
The permutation group isomorphic to [Z.sub.3] contains the permutation matrices 7, X, and [X.sup.2] of the Pauli group, where X is the shift matrix in (1).
Let P = {1, 2, ..., 10} and G = [M.sub.10], [PGL.sub.2](9) or [PGL.sub.2](9) be the primitive permutation group of degree 10 acting on P.
Symmetry reduction theory based on permutation group is reported in Section 6.
(3) In the type B process, which is a variant of the carries process, the stationary distribution is proportional to the Macmahon number, which gives us the statistics of the type B-descent of the hyperoctahedral group (signed permutation group).
In fact, the action of [S.sub.3], the permutation group in tree elements, preserves the configuration of six points in Fig.
It is a natural extension of (3) from the viewpoint of absolute mathematics, because the symmetric group is interpreted as [S.sub.n] = GL(n,[F.sub.1]), and the generalized permutation group is [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
If the right nucleus [N.sub.r](Q) is a normal subgroup, then the equivalence relation induced by the orbits ofthe right-regular permutation group R([??]) is a normal congruence.
An important class of functions comes from permutation groups. The orbital profile of a permutation group G acting on a set E is the function [[theta].sub.G] which counts for each integer n the number, possibly infinite, of orbits of the n-element subsets of E.
A subgroup of [S.sub.X] is called a permutation group on X.
If the identification group of each structure in !K.sup.P^ coincides with the permutation group, then all the members of !K.sup.P^ are co-intended.
A hypermap is a pair of permutations ([sigma], [alpha]) on a set {1,2, ..., n}, generating a transitive permutation group. Its genus g([sigma], [alpha]), a nonnegative integer (see ) is defined by

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