Finite Geometry Notes
|76-08-??...||Diamond theory cover page From the author's 1976 booklet. See Math16.com for the meaning of the cover illustration.|
|78-??-??...||Research announcement (4x4 case of diamond theorem and algebraic generalization) This research announcement was the basis for an abstract (79T-A37) in the Feb. 1979 AMS Notices.|
|78-12-??...||Orthogonality of Latin squares viewed as skewness of lines Structural diagrams of 4x4 arrays play the role of lines in PG(3,2). Orthogonality of arrays corresponds to skewness of lines.|
|82-06-12...||Inscapes A new combinatorial way of illustrating symplectic polarities in PG(3,2).|
|82-09-22...||Inscapes II The concept in "Inscapes" is generalized.|
|83-06-21...||An invariance of symmetry The diamond theorem on a 4x4x4 cube, and a sketch of the proof.|
|83-10-01...||Portrait of O A table of the octahedral group O using the 24 patterns from the 2x2 case of the diamond theorem.|
|83-10-16...||Study of O A different way of looking at the octahedral group, using cubes that illustrate the 2x2x2 case of the diamond theorem.|
|84-09-15...||Diamonds and whirls Block designs of a different sort -- graphic figures on cubes. See also the University of Exeter page on the octahedral group O.|
|84-09-25...||Affine groups on small binary spaces Six ways to slice a cube, and the resulting affine groups. For details, see the author's 1984 paper Binary Coordinate Systems.|
|85-03-26...||Visualizing GL(2, p)|
|85-04-28...||Generating the octad generator The Miracle Octad Generator (MOG) of R. T. Curtis -- A correspondence between the 35 partitions of an 8-set into two 4-sets and the 35 lines of PG(3,2).|
|85-08-22...||Symmetry invariance under M12 A generalization of the two-color plane patterns, made up of all-black and all-white squares, that underlie plane patterns, made up of two-color diagonally-divided squares, of diamond theory.|
|86-02-04...||Inscapes III: PG(2,4) from PG(3,2)|
|86-04-26...||Picturing the smallest projective 3-space A symplectic polarity, the Conwell-Curtis correspondence, and the large Mathieu group.|
related to M24 Anatomy of the polarity pictured in
the 86-04-06 note.
2-subsets of a 6-set are the points of a PG(3,2)
Beutelspacher's model of the 15 points of PG(3,2) compared with a 15-line complex in PG(3,2).
projective partitions The author's model of the 21-point projective
For a general method of constructing such models, see Modeling the 21-point plane with outer automorphisms of S6.
The following problem was suggested by the above.
PROBLEM: Let M be an nxn square (0,1) matrix with exactly k 1's in each row and each column. What conditions are necessary and sufficient for there to exist row/column permutations that make M a symmetric matrix?
For more on this problem, see Duality and Symmetry.
automorphism of S6 related to M24 An
application of the "inscape" model of a generalized quadrangle to the
construction of the large Mathieu group.
automorphisms of S6 An application of the
"inscape" model to S6.
|86-07-11...||Inscapes IV An outer automorphism that is literally outer.|