We shall denote the set of all full linear orderings of by . A duality that respects the orderings in question is known as a Galois connection. The same notation can apply for two different hypothetical orderings of the same voter. That is, using this format textual orderings and chronological orderings are identical. Here sup is the supremum with respect to the orderings in "X" and "Y", respectively. Various chronological orderings and lists of kings have been proposed by scholars for this dynasty. Nahuatl allows all possible orderings of the three basic sentence constituents. General treatment of orderings that minimize fill-in can be addressed using graph theory. Multiple orderings are then sampled and evaluated. Other magnetic orderings, such as spin glass ordering, also exhibit this phenomenon. The interest of the book is in amalgamating sets of orderings. And is well-ordered by the ordered sum (indexed by ) of the orderings on . The graph of moves on these 13 weak orderings is shown in the figure. These are all the possible orderings of this three-element set. The table shows which orderings are admitted.