
Case Study of Nonsymmetric Binary Cubic Operads 301
case parameters nilpotent |X|
k
percentage
1 6 1768810 1771561 ≈ 99.845
2 5 160662 161051 ≈ 99.758
3 4 14636 14641 ≈ 99.966
4 4 14570 14641 ≈ 99.515
5 3 1310 1331 ≈ 98.422
Closer inspection of these results shows that we can obtain nilpotent operads
even when only one of the parameters is nonzero. Since this special case has
only one parameter, we can make the corresponding substitutions into the
quartic relation matrix C, and compute its Smith normal form. In all cases
the minimal rank is 12, and so the first 12 diagonal entries of the Smith form
are 1; we are only concerned with the last two diagonal