[5927] in cryptography@c2.net mail archive
size of linear function space
daemon@ATHENA.MIT.EDU (staym@accessdata.com)
Mon Oct 18 19:43:50 1999
From: staym@accessdata.com
Message-ID: <380BA715.3925@accessdata.com>
Date: Mon, 18 Oct 1999 17:02:45 -0600
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Consider functions of one variable whose domain and range are both
{0,1,2,...,n-1}. There are n^n possible functions. 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; I'm interested in the sum
over all definitions of + that satisfy the usual requirements of
associativity, commutativity, additive identity, etc.
--
Mike Stay
Programmer / Crypto guy
AccessData Corp.
mailto:staym@accessdata.com
