Minimizing the sum(permutation*inverse)
zak seidov
zakseidov at yahoo.com
Mon May 15 21:40:29 CEST 2006
Yes, of course,
it'd be numbers not digits -
as i suggested
Zak
--- franktaw at netscape.net wrote:
> These aren't finite sequences; just the first 9
> terms of two infinite sequences. Permutations are
> of numbers, not digits.
>
> The second one is A000330.
>
> Franklin T. Adams-Watters
>
>
> -----Original Message-----
> From: zak seidov zakseidov at yahoo.com
>
>
> Here's table of min and max for n=1...9 (first
> entry)
>
> {1,1,1}
> {2,5,5}
> {3,11,14}
> {4,20,30}
> {5,35,55}
> {6,57,91}
> {7,85,140}
> {8,120,204}
> {9,165,285}
> which gives two full fini seqs:
>
> 1, 5, 11, 20, 35, 57, 85, 120, 165,
> 1, 5, 14, 30, 55, 91, 140, 204, 285
>
> Zak
>
> --- Leroy Quet <qq-quet at mindspring.com> wrote:
>
> > Regarding the sci.math thread:
> >
> >
>
http://groups.google.com/group/sci.math/browse_thread/thread/6cf265b0d0e2f1
> > 57
> >
> > Let {b(k)} be a permutation of {1,2,3,...,n}.
> > Let {c(k)} be the inverse-permutation of {b(k)}.
> > (ie. b(c(j)) =j, for every j.)
> >
> > What is the minimum possible sum:
> > sum{k=1 to n} b(k) * c(k) ?
> >
> > For example, if b is:
> > [1,2,3],
> > [2,1,3],
> > [3,2,1],
> > each give a sum of 14 (since each of these
> > permutations is its own
> > inverse).
> >
> > But
> > [2,3,1],
> > [3,1,2],
> > (which are inverses of each other)
> > both give a sum of 11.
> >
> > I get (possibly erroneously) that the sequences of
> > minimum sums begins:
> > 1, 5, 11, 20, 35,...
> >
> > Could someone please calculate/submit this
> sequence
> > (unless it is already
> > in the EIS, of course).
> >
> > thanks,
> > Leroy Quet
> >
>
>
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