bijections between graphs

Hello,


I have a naive question that I already find difficult to phrase properly.


I am interested in certain combinatoric problems that involve constructing
bijections (one-to-one, or reversible) maps from one set of graphs
characterized in a certain way to another set of graphs.


These graphs are typically Ferrer diagrams, which one uses in order to
represent generating functions of partitions (different ways to represent
a number as the sum of other numbers) that satisfy certain conditions.


The problem is typically one describes these maps in a verbal way, that
tends to get confusing for serious problems, and one has to proceed in
terms of explicit numerical examples, and it is never clear if these
examples are sufficiently general.


What is even more problematic is to "prove" that such maps is well
defined, and reversible.


I am looking for a better way to phrase/study these maps.


I would like to think of what I am doing as a translation from one
language to another using well-defined rules, and that the map is an
automaton that does the translation.


I would like to use ideas from the theory of languages and machines to
re-phrase my work in a better and more precise language. But if this makes
any sense, then it cannot be totally new.


My question is: is there any work that is already done that you know of
that looks into similar problems?


Thank you in advance,


Omar Foda.
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