In general, for a subcoset Hy [subset or equal to] Gx (using the notation Hy even if it may be empty), when generators for H and a coset representative
are not necessarily available at hand, if we are given a polynomial-time procedure to determine, for any given z [member of] Gx, whether z [member of] Hy, then we say Hy is (polynomial-time) recognizable.
If I is the order ideal encircled by the solid line, then [phi](I) is the coset representative
encircled by the solid line, and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is labeled by [S.
I] [member of] W is the unique coset representative
of minimum (affine) length.
When we wish to refer to the Poincare polynomial of a minimal length coset representative
w for the induced order on either of the quotients [sup.
In our case, the base window of the minimal length coset representative
of an element is obtained by ordering the entries that appear in the base window increasingly.
1, every coatom w is a maximal-length coset representative
of the subgroup [W.
The authors cover convex preorders and cuspidal systems, imaginary representations, imaginary Schur-Weyl duality, imaginary Howe and Ringel dualities, Gelfand-Graev words and representations, partitions and compositions, Coset representatives
, Schur algebras, and a wide-ranging variety of other related mathematical subjects.
i]} be a distinct set of coset representatives
A set K formed by a collection of such representatives is called a transversal, and by definition K consists of one and just one point from each distinct coset H + a = [a] (the transversal is also called a complete set of coset representatives
but we shall stick to the shorter name).
Furthermore, in order to resolve the scaling problems of Wyler's expression, Gilmore showed why it is essential to use dimensionless volumes by setting the throat sizes of the Anti de Sitter hyperboloids to r = 1, because this is the only choice for r where all elements in the bounded domains are also coset representatives
, and therefore, amount to honest group operations.
The minimal length left coset representatives
[omega] [member of] [[?
J] the set of minimum-length coset representatives