[seqfan] Re: Nathaniel Johnston's "orderings of pairs" A237749.

Max Alekseyev maxale at gmail.com
Wed Feb 19 14:00:45 CET 2014


There are two other sequences of this kind: A231074 and A231085. But they
address products/sums only of distinct terms, while A237749 allow equal
terms.

Regards,
Max

On Feb 18, 2014 10:08 AM, "Neil Sloane" <njasloane at gmail.com> wrote:
>
> Hans, nice work!
> I guess the connection with the original problem is
> that we replace the x's by their logs, say y_i = log x_i,
> and now we look at the number of different
> orderings of the pairwise sums y_i + y_j ?
>
>
> On Tue, Feb 18, 2014 at 9:49 AM, Hans Havermann <gladhobo at teksavvy.com
>wrote:
>
> > "... the number of combinatorially different Golomb rulers with a given
> > number of markings (this sequence starts with 1, 2, 10, 114, 2608, and
> > 107498)."
> >
> > The sequence appears in Tu Pham's May 2011 thesis (Enumeration of Golomb
> > Rulers):
> >
> > "This means the projected region is precisely described by the
hyperplane
> > arrangement H(m). Hence we conclude the projected region is a region of
> > G(m).
> >
> > By using a program to compute the number of regions of an inside-out
> > polytope written by Andrew Van Herick[3], we were able to compute the
> > number of regions of G(m) where m ranges from 1 to 6.
> >
> > m   R(m)
> > 1      1
> > 2      2
> > 3     10
> > 4    114
> > 5   2608
> > 6 107498
> >
> > Table 3.1: The number of regions of G(m)."
> >
> > The reference [3] is to Matthias Beck and Andrew van Herick, Enumeration
> > of 4 × 4 magic squares, Math. Comp. 80 (2011), no. 273, 617-621. MR
2728997.
> >
> > _______________________________________________
> >
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> >
>
>
>
> --
> Dear Friends, I have now retired from AT&T. New coordinates:
>
> Neil J. A. Sloane, President, OEIS Foundation
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
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>
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