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

Neil Sloane njasloane at gmail.com
Tue Feb 18 16:07:53 CET 2014


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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>



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