tag:blogger.com,1999:blog-5195188167565410449.post7958819987416747163..comments2014-03-09T17:09:45.698ZComments on Haskell for Maths: Finite geometries, part 2: Symmetries of AG(n,Fq)DavidAhttp://www.blogger.com/profile/16359932006803389458noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-5195188167565410449.post-12410321684807754652009-10-02T21:40:55.369+01:002009-10-02T21:40:55.369+01:00m759:
You misunderstand my claim. I agree that the...m759:<br />You misunderstand my claim. I agree that there are only 322560 affine transformations of AG(4,F2). I'm asking what are the symmetries of AG(4,F2) *considered as an incidence structure*. Certainly the affine transformations will be among them. However, a little thought shows that as an incidence structure, AG(4,F2) is equal / isomorphic to the complete graph K16. Hence it has 16! symmetries (where a symmetry of an incidence structure is a permutation of the points that preserves the lines collectively). Not all of these are affine transformations of course, just as not all symmetries of AG(2,F4) were affine transformations (some were field automorphisms).DavidAhttp://www.blogger.com/profile/16359932006803389458noreply@blogger.comtag:blogger.com,1999:blog-5195188167565410449.post-86828251796672517372009-10-02T01:30:52.054+01:002009-10-02T01:30:52.054+01:00Actually, AG(4,2) has, not 16!, but only 322,560 &...Actually, AG(4,2) has, not 16!, but only 322,560 "symmetries"-- i.e., affine transformations. See diamondtheorem.com and various introductory works on finite geometry.m759http://www.blogger.com/profile/18291853371291950138noreply@blogger.com