## Bijection from (Z_n)^3 to (Z_n)^2

For the discussion of math. Duh.

Moderators: gmalivuk, Moderators General, Prelates

Dynotec
Posts: 89
Joined: Fri Dec 15, 2006 2:13 pm UTC
Contact:

### Bijection from (Z_n)^3 to (Z_n)^2

I'm looking for a nice bijection from {1,...,n}^3 to {1,...,n}^2. I'm hoping to use it for a hack with an unfortunate statistical modeling program that doesn't handle vectors very well beyond two dimensions.

The Sleeping Tyrant
Posts: 533
Joined: Tue Jan 23, 2007 2:49 am UTC
Contact:

### Re: Bijection from (Z_n)^3 to (Z_n)^2

I'm afraid that whenever n is bigger than 1 there isn't any bijection between them, since the first contains n^3 elements while the second has only n^2 elements.

Dynotec
Posts: 89
Joined: Fri Dec 15, 2006 2:13 pm UTC
Contact:

### Re: Bijection from (Z_n)^3 to (Z_n)^2

The Sleeping Tyrant wrote:I'm afraid that whenever n is bigger than 1 there isn't any bijection between them, since the first contains n^3 elements while the second has only n^2 elements.

Yes, of course. I feel dumb having asked the question. What about from {1,...,n}^3->{1,...n}x{1,...,n^2}?

jestingrabbit
Factoids are just Datas that haven't grown up yet
Posts: 5967
Joined: Tue Nov 28, 2006 9:50 pm UTC
Location: Sydney

### Re: Bijection from (Z_n)^3 to (Z_n)^2

There's always the natural bijection, (a,b,c) -> (a, (b,c)). There are also a myriad other maps. What sort of thing are you looking for?

edit: misread the problem, saw the ^2 as outside the }. Gmal's is right.
Last edited by jestingrabbit on Sun May 29, 2011 7:39 pm UTC, edited 1 time in total.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

Dynotec
Posts: 89
Joined: Fri Dec 15, 2006 2:13 pm UTC
Contact:

### Re: Bijection from (Z_n)^3 to (Z_n)^2

jestingrabbit wrote:There's always the natural bijection, (a,b,c) -> (a, (b,c)). There are also a myriad other maps. What sort of thing are you looking for?

A simple easily computable and invertible function that takes a three-tuple of integers and returns a two-tuple of integers.

gmalivuk
GNU Terry Pratchett
Posts: 26820
Joined: Wed Feb 28, 2007 6:02 pm UTC
Location: Here and There
Contact: