Veit, You're right, I mistranscribed it. My software is running on our "inside" system with no connection to the internet, so I have to retype things. The run for f(6) just finished with 32 solutions, 3 of which have denominator 120 and the rest denominator 60. Cplex actually found 227 solutions for f(5) -- but that was counting a solution as different if it had different partitions (aka colorings) for division into 3, 4 and 5. For f(6) it found 7947 solutions before ignoring which way they were partitioned into 4,5,6 pieces. So you might have fun trying to reassemble the 18 into essentially different ways. After New Year's I'll write some programs to give finer statistics about them. Victor PS. To Warren. I had already put a feature in my program to restrict the partitions considered at various levels. For the full f(6) it took a 2563 seconds to find all solutions. But, when I restricted the 6-partition to (1,1,1,2,3,3) (since the value of f(6) is 11), it took only 13 seconds to find 3780 solutions satisfying that partition). On Fri, Dec 29, 2017 at 5:03 PM, Veit Elser <ve10@cornell.edu> wrote:
The sharp-eyed among you may have noted that my denominator 240 solution for f(5) was spurious, since it has 10 parts and not 9. The f(5) solutions are (after multiplying by 60):
(1, 5, 6, 11, 13, 17, 19, 23, 24)/2 If you’re trying to catch us asleep again, then you've failed. That 6 should be a 7.
-Veit
P.S. Does your software let you know how many solutions there are for each partition? If so, it could explain the rather non-uniform rates that divide-and-concur finds them. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun