[5931] in cryptography@c2.net mail archive
Re: size of linear function space
daemon@ATHENA.MIT.EDU (Ben Laurie)
Tue Oct 19 11:07:42 1999
Message-ID: <380C3FD9.FB433129@algroup.co.uk>
Date: Tue, 19 Oct 1999 10:54:33 +0100
From: Ben Laurie <ben@algroup.co.uk>
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To: staym@accessdata.com
Cc: cryptography@c2.net, coderpunks@toad.com
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staym@accessdata.com wrote:
>
> Consider functions of one variable whose domain and range are both
> {0,1,2,...,n-1}. There are n^n possible functions.
n!, I'd say, since the range of any function that isn't one-to-one is
_not_ {0..n-1}. Did you mean that the range was a subset of {0..n-1}? Or
perhaps (equivalently) you meant to say "codomain" instead of "range"?
> How many of these
> are linear [i.e. F(a+b) = F(a) + F(b) + c, where c is the same for all
> a,b (if it were different, that would be trivial)]? For any one
> definition of +, there will be some number;
This strikes me as completely false. Can't be bothered to prove it,
though. Especially since the problem is currently not well-defined :-)
> I'm interested in the sum
> over all definitions of + that satisfy the usual requirements of
> associativity, commutativity, additive identity, etc.
Hmm. This is horribly inexact. Do you mean the usual requirements for a
group? A field? What?
And like anonymous says, if you are going to ask these weird questions
(some of which are quite entertaining), you could at least say why.
Cheers,
Ben.
--
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"My grandfather once told me that there are two kinds of people: those
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