Given any uniformly random matrix A [member of] [Z.sup.nxm.sub.q], a zero vector 0 [member of] [Z.sup.n.sub.q], and any syndrome u [member of] [Z.sup.n.sub.q], a q -ary lattice [[and].sup.[perpendicular to].sub.q] (A) and a
coset [[and].sup.u.sub.q] (A) of [[and].sup.[perpendicular to].sub.q] (A) are defined as follows:
For [[GAMMA].sup.+.sub.0] (p), we have the disjoint union of double
cosets,
This is done by using the definition of [PHI], the triangle inequality, the
coset decomposition formula and the Cauchy-Schwarz inequality, as follows:
Numerous hypergroups, well known in the literature, which form wide classes as join spaces, weak cogroups, double
cosets spaces, polygroups and canonical hypergroups including usual groups and also some geometrically motivated non-commutative hyperstructures--belong to transposition hypergroups.
Since G is residually finite, by Lemma 4 there exists a subgroup H [less than or equal to] G of finite index such that H [intersection] EN = H [intersection] N = {1} : if J is a set of representatives of the right
cosets of H such that EN [subset or equal to] J, then
The original algorithm conauto [19] solves the GI problem but not the GA problem; conauto-2.0 is a modified version that computes automorphism groups and uses limited, though quite effective,
coset and orbit pruning.
Torstensson, "
Coset diagrams in the study of .nitely presented groups with an application to quotients of the modular group," Journal of Commutative Algebra, vol.
Generic points of the quadrangle are elements of the group, generic lines are left (or right-the choice does not change the isomorphism class of the geometry)
cosets of the subgroups of type [E.sub.i], and some other special points and lines exist.
In particular there are n + 1 double
cosets of the parabolic Weyl group [S.sub.n], accounting for the n + 1 non-isomorphic partial dualizations on subgroups [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for k = 0,...
For any
coset [mathematical expression not reproducible], and probability zero elsewhere.
British economist, cost, cosine,
coset, coot, the surrounding waters the of regions all cons, cone, comet, comes, come, coins, -Portland Rockall, Cromarty, R.
Where convenient, the author is treating elements of Z/B as simple integers rather than entire
cosets. The smallest nonnegative member of the
coset is used for the address.