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Friday, December 20, 2013

For Emil Artin

Filed under: General,Geometry — Tags: , — m759 @ 12:00 PM

(On His Dies Natalis )

An Exceptional Isomorphism Between Geometric and
Combinatorial Steiner Triple Systems Underlies 
the Octads of the M24 Steiner System S(5, 8, 24).

This is asserted in an excerpt from… 

"The smallest non-rank 3 strongly regular graphs
​which satisfy the 4-vertex condition"
by Mikhail Klin, Mariusz Meszka, Sven Reichard, and Alex Rosa,
BAYREUTHER MATHEMATISCHE SCHRIFTEN 73 (2005), 152-212—

(Click for clearer image)

Note that Theorem 46 of Klin et al.  describes the role
of the Galois tesseract  in the Miracle Octad Generator
of R. T. Curtis (original 1976 version). The tesseract
(a 4×4 array) supplies the geometric  part of the above
exceptional geometric-combinatorial isomorphism.

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