TITLE: Definition of infinite permutations
QUESTION [7 upvotes]: I've been trying to find a definition of an infinite permutation on-line without much success. Does there exist a canonical definition or are there various ways one might go about defining this?
The obvious candidate I guess would be a bijection p : {1,2,...} -> {1,2,...} between the natural numbers. One might also try to use the Robinson-Schensted correspondence between permutations of length n and pairs of standard Young tableaux of size n. Then one would need a definition of infinite Young tableaux.
Another correspondence that might be used is between permutations and permutation matrices.

REPLY [2 votes]: You might also be interested in the "juggling patterns" of Knutson, Lam, and Speyer, defined here: http://arxiv.org/abs/1111.3660.
Also known as bounded affine permutations, these are a subset of the affine permutations that Lusztig introduced mentioned by Igor Pak. Namely, they are the affine permutations $\Sigma_n$ (so $\pi$ a permutation $\mathbb{Z} \to \mathbb{Z}$ with $\pi(i+n) = \pi(i)+n$) that also satisfy $i \leq \pi(i) \leq i + n$. They are related to total positivity and the positroid stratification. There is a nice way to visualize them as juggling patterns, where the number of balls being juggled is equal to the average $\frac{1}{n}\sum_{i=1}^{n}(f(i) -i)$.