Progress in generating configurations with n odd
On 29.12.1996 a new idea came to my mind. Unbelievable why not earlier!
When I looked at the nearest symmetry misses of rot4 configurations, I realized
that these configurations (rot2 upto n = 25 computed) have odd n (trivial) and ALWAYS missed the symmetry on a long diagonal. Further from n=17 starting, there was at least one such configuration upto n equals 25.
On the next day, the 30th December, I wrote a first program, developed from my rot4-nothree, which searches for configurations with odd n and have rot4 symmetry but the long diagonals. And immediatly there were discovered some new configurations for
n = 27, 29 and 31. On Sylvester I wrote a new variante of this nearest-rot4-nothree, which generates all solutions for odd n as fast as the rot4-nothree for even (n+1).
When starting at the evening I was present when it generated all solutions for n= 27,28,29,31,33. When I went the runs with n=35 and n=37
were started and only a solutions for n=35 was found.
New Year's Eve
New Year
On the afternoon of 1st January I had the next look at my program results. The
n=35 case was completed with a total of 23 new solutions and 10 new configurations with n=37 were found. I believe I will never know whether the first 37-configurations was found in 1996 or in 1997. :)
Meanwhile n=39 and n=41 configurations are found and my excitement has cooled down. Because there are not as many in this new symmetry class, call it 'rct4', as in
'rot4' for even n, I will be glad to find solutions upto n=45 in reasonable cputime.
This new class, which is not a symmetry class of the grid, will have its own symmetry-character c in its coded representation. Whether other almost symmetric classes will be introduced, this decision is pushed into the future.
It is now January, 31th and today the first n=45 configuration has been discovered after n=43 was discovered at January, 12th. Further the new class 'rct4' is
integrated into the encoding & decoding routines.
Achim Flammenkamp
97-02-02 14:00