Log24

Wednesday, June 1, 2011

The Schwartz Notes

Filed under: General,Geometry — Tags: , — m759 @ 2:00 PM

A Google search today for material on the Web that puts the diamond theorem
in context yielded a satisfyingly complete list. (See the first 21 results.)
(Customization based on signed-out search activity was disabled.)

The same search limited to results from only the past month yielded,
in addition, the following—

http://www.log24.com/log/pix11A/110601-Search.jpg

This turns out to be a document by one Richard Evan Schwartz,
Chancellor's Professor of Mathematics at Brown University.

Pages 12-14 of the document, which is untitled, undated, and
unsigned, discuss the finite-geometry background of the R.T.
Curtis Miracle Octad Generator (MOG) . As today's earlier search indicates,
this is closely related to the diamond theorem. The section relating
the geometry to the MOG is titled "The MOG and Projective Space."
It does not mention my own work.

See Schwartz's page 12, page 13, and page 14.

Compare to the web pages from today's earlier search.

There are no references at the end of the Schwartz document,
but there is this at the beginning—

These are some notes on error correcting codes. Two good sources for
this material are
From Error Correcting Codes through Sphere Packings to Simple Groups ,
by Thomas Thompson.
Sphere Packings, Lattices, and Simple Groups  by J. H. Conway and N.
Sloane
Planet Math (on the internet) also some information.

It seems clear that these inadequate remarks by Schwartz on his sources
can and should be expanded.

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