Up
Proper Sequences and Suitable Origins

Definition A sequence of shift and inverse shift operators , , , , , , , and is a proper sequence if the composition is defined. 

Definition A quadruple is a suitable origin if and are disjoint.  (Hence, , , , and .)

Definition A quadruple is accessible from a quadruple if there exists a constant and a proper sequence of shift and inverse shift operators , , , , , , , and such that