Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question

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,

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.