Max/Min Sums From Permutations

[Joshua Zucker]

I very much like Emeric's suggestion that we look at the circular
version of this sequence!

I haven't been able to get very much farther, though, and there's not
as simple of an obvious conjecture about the sequence; I'll have to
keep thinking.  Has anyone got anything better than the brute-force
computer search yet?

As for the sequence of mins already being in there, the comments from
the sequence Rainer pointed out will lead you pretty quickly to
http://www.research.att.com/projects/OEIS?Anum=A006527 whereupon the
comment of Clark Kimberling's about the dot product form makes this
obviously the same as my conjecture.

Thanks everyone for all the fun here at seqfan,
--Joshua Zucker

On Sat, 29 Jan 2005 18:18:34 +0100, Rainer Rosenthal <r.rosenthal at web.de> wrote:
> http://www.research.att.com/projects/OEIS?Anum=A026035