# Indexing/Ranking in Combinatorics

Which terms are used for the problem of mapping each element of a finite set $S$ one-to-one to a natural number in $\{0, \ldots, |S|-1\}$?

I am thinking of non-trivial sets, of course, such as the set of all connected subgraphs of a given graph.

Enumeration, indexing, ranking?

Are there any text books, journals, theses on this subject in general?

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## 1 Answer

It's usually enumeration. The subject enumerative combinatorics is relevant, although I think it does not always seek bijection with a subset of integers: having a bijection with a subset of known size is enough.

But in your case the problem is really algorithmic : you seek an exhaustive enumeration algorithm. Here StackOverflow is more likely to help. For example, http://stackoverflow.com/questions/5984531/subgraph-enumeration

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