G [less than or equal to] Sym([OMEGA]), is specified by a pair consisting of generating sets for G and K, and an element g [member of] G is specified by a coset representative g [member of] G such that g = Kg.
c]) for a constant c > 0 (specified by a polynomial-time procedure to test, for given g [member of] G, whether g [member of] H), find generators for H and a complete set of coset representatives for H in G.
Let WJ be the maximal parabolic subgroup of W stabilizing A, and let WJ be the set of minimum-length coset representatives
for the parabolic quotient W/[W.
We define the ish statistic in terms of minimal coset representatives
The set of all minimal length coset representatives
We associate an abacus to each minimal length coset representative
w [member of] [[?
By a slight abuse of notation, we will refer to the set of minimal length left (right) coset representatives
af] is the set of minimum-length coset representatives
k] denote the set of minimal-length coset representatives
a set of stable and recurrent configurations that form a set of coset representatives
for the critical group.
This allows us to use tools from Coxeter groups, for example the Bruhat order, parabolic subgroups, and minimal coset representatives
J] in terms of maximal coset representatives
v, w [member of] [W.