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Note that the only state satisfying AGp is the state c; however, the structure does not satisfy AF{c}-as shown in the right hand side of the figure, the left most path of the computation tree is a counterexample. On this particular path, we can stay in the state a while reserving ...
Consider a bipartition of the set S=S −⊔S + such that any two generators in S ϵ commute (this is possible since the graph of the Coxeter group is a tree), then form the Coxeter element c ∗=c − c +, where \(c_{\epsilon}=\prod_{s\in S_{\epsilon}}s\). Using ...