Actual results

Up to this point (March 1997) I have been able to make my program run for cutoff parameters NF less or equal to 15. The actual results came out as follows.

Cross. num. |   0   1   2   3   4   5   6   7   8   9    10    11    12     13      14      15
-------------------------------------------------------------------------------------------------- 
Output Knots    
               
NF  =   0   |   1    
NF  =   1   |   1   0
NF  =   2   |   1   0   0
NF  =   3   |   1   0   0   1
NF  =   4   |   1   0   0   1   1
NF  =   5   |   1   0   0   1   1   2
NF  =   6   |   1   0   0   1   1   2   3
NF  =   7   |   1   0   0   1   1   2   3  13
NF  =   8   |   1   0   0   1   1   2   3   7  45
NF  =   9   |   1   0   0   1   1   2   3   7  21 223 
NF  =  10   |   1   0   0   1   1   2   3   7  21  54  1120
NF  =  11   |   1   0   0   1   1   2   3   7  21  49   220  6948 
NF  =  12   |   1   0   0   1   1   2   3   7  21  49   165   945 44321
NF  =  13   |   1   0   0   1   1   2   3   7  21  49   165   555  5050 304492
NF  =  14   |   1   0   0   1   1   2   3   7  21  49   165   552  2191  29781 2145612
NF  =  15   |   1   0   0   1   1   2   3   7  21  49   165   552  2176  10363  305317 15543241       

As expected, the number of output knots decreases as the cutoff parameter NF increases, until only the truly distinct knots remain. To see how knots with crossing numbers up to 12 are shown distinct, click . (Technical remarks: For NF=15: Memory needed is about 20 MBytes, CPU time is about one month, computer language used is f77, the program is run at the Orion machine at the Deutsches Elektronen SYnchrotron D.E.SY. at Zeuthen, Germany).

Charilaos Aneziris, charilaos_aneziris@standardandpoors.com

Copyright 1996

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