Log24

Saturday, May 8, 2021

A Tale of Two Omegas

Filed under: General — Tags: , — m759 @ 5:00 am

The Greek capital letter Omega, Ω, is customarily
used to denote a set that is acted upon by a group.
If the group is the affine group of 322,560
transformations of the four-dimensional
affine space over the two-element Galois field,
the appropriate Ω is the 4×4 grid above.

See the Cullinane diamond theorem .

If the group is the large Mathieu group  of
244,823,040 permutations of 24 things,
the appropriate Ω  is the 4×6 grid below.

See the Miracle Octad Generator  of R. T. Curtis.

Sunday, May 6, 2018

The Osterman Omega

Filed under: General,Geometry — Tags: , — m759 @ 5:01 pm

From "The Osterman Weekend" (1983) —

Counting symmetries of the R. T. Curtis Omega:

An Illustration from Shakespeare's birthday

Counting symmetries with the orbit-stabilizer theorem

Friday, September 30, 2022

Classics Illustrated: The Bitmap File  by Harlan Kane

Filed under: General — m759 @ 10:21 am

Related Log24 posts

See Vox Lux and Mathieu Omega.

Related book cover

Tuesday, August 26, 2014

Lux et Veritas

Filed under: General,Geometry — m759 @ 7:59 am

Omega by Lux:

Mathieu and Omega Steps

Omega by Curtis:

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