Date: Around 1995
Taking an ordered set, like a text (in a text, the letters must keep a
certain order, if they shall carry any information) I would like to find an
algebraic structure so that I can "compress" it or classify it or whatever.
I think, that it is not too improbable that there is some kind of formalized
structure in many kinds of ordered sets. The reason I asked if and ordered
group would always be cyclic is, that I assume that the morphisms on such
groups should preserve order as well as group structure. I cannot quite
figure out, if one can construct an ordered ordering that will not enforce
other properties on.
OK, let us try again. I think that you are not using the customary
definition of the word "order". A set is well-ordered if, given any 2
members of the set I can decide whether the objects are equal or, if not,
which one is greater.
You have identified your problem as being related to data compression.
There is an introduction to this topic in Liu's book on Combinatorics. I
can give you a more detailed reference if need be.
You use the term "group", so I do not know how you give text the
properties of a group.
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