Illustration by Nicholas Konrad / The New Yorker April 28, 2022
Some related material from Harvard —
Friday, April 29, 2022
Metamorphosis: Seed to Flower in New Yorker Propaganda
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Friday, March 29, 2019
Front-Row Seed
"This outer automorphism can be regarded as
the seed from which grow about half of the
sporadic simple groups…." — Noam Elkies
Closely related material —
The top two cells of the Curtis "heavy brick" are also
the key to the diamond-theorem correlation.
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Monday, June 24, 2024
Thursday, June 2, 2022
The Separatrix: 6/2
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Tuesday, February 26, 2019
Citation
Some related material in this journal — See a search for k6.gif.
Some related material from Harvard —
Elkies's "15 simple transpositions" clearly correspond to the 15 edges of
the complete graph K6 and to the 15 2-subsets of a 6-set.
For the connection to PG(3,2), see Finite Geometry of the Square and Cube.
The following "manifestation" of the 2-subsets of a 6-set might serve as
the desired Wikipedia citation —
See also the above 1986 construction of PG(3,2) from a 6-set
in the work of other authors in 1994 and 2002 . . .
-
Gonzalez-Dorrego, Maria R. (Maria del Rosario),
(16,6) Configurations and Geometry of Kummer Surfaces in P3.
American Mathematical Society, Providence, RI, 1994. -
Dolgachev, Igor, and Keum, JongHae,
"Birational Automorphisms of Quartic Hessian Surfaces."
Trans. Amer. Math. Soc. 354 (2002), 3031-3057.
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Monday, September 4, 2006
Monday September 4, 2006
In a Nutshell:
The Seed
The Seed
"The symmetric group S6 of permutations of 6 objects is the only symmetric group with an outer automorphism….
This outer automorphism can be regarded as the seed from which grow about half of the sporadic simple groups…."
This "seed" may be pictured as
within what Burkard Polster has called "the smallest perfect universe"– PG(3,2), the projective 3-space over the 2-element field.
Related material: yesterday's entry for Sylvester's birthday.
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Saturday, March 11, 2006
Saturday March 11, 2006
Seed
"This outer automorphism [of S6] can be regarded as the seed
from which grow about half of the sporadic simple groups,
starting with the Mathieu groups M12 and M24."
Feb. 28 (Mardi Gras), 2006.
Related material:
For details, click on the Six of One.
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