Tuples

This article page is a stub, please help by expanding it.

---

A tuple is an ordered list of elements. That is, it is a finite sequence.

There are various ways to encode in a nonnegative integer a tuple of nonnegative-integers or natural numbers of an arbitrary, but finite length. These include the binary run-length encoding or using exponent-tuple of the prime factorization. To encode specific $\scriptstyle n\,$-tuples (i.e. of the fixed length) see Marc LeBrun's method explained in A000695.

To encode a tuple of integers (including zero and negative numbers) of an arbitrary, but finite length, one can use the factorization of a positive rational number to its integer prime factors, and then use one of the orderings of rational numbers like Stern-Brocot tree to map them to nonnegative integers.