exact formula for N(lam, nu) = brute force count for 3 <= n <= 7: True
n=3: 3 x 3 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 1 (0.0 s)
n=4: 5 x 5 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 1 (0.0 s)
n=5: 7 x 7 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 1 (0.0 s)
n=6: 11 x 11 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 1 (0.0 s)
n=7: 15 x 15 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 1 (0.0 s)
n=8: 22 x 22 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 1 (0.0 s)
n=9: 30 x 30 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 1 (0.0 s)
n=10: 42 x 42 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 1 (0.0 s)
n=11: 56 x 56 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 1 (0.0 s)
n=12: 77 x 77 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 2 (0.0 s)
n=13: 101 x 101 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 2 (0.0 s)
n=14: 135 x 135 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 2 (0.0 s)
n=15: 176 x 176 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 2 (0.0 s)
n=16: 231 x 231 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 2 (0.0 s)
n=17: 297 x 297 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 3 (0.0 s)
n=18: 385 x 385 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 3 (0.0 s)
n=19: 490 x 490 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 3 (0.0 s)
n=20: 627 x 627 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 3 (0.0 s)
n=21: 792 x 792 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 3 (0.0 s)
n=22: 1002 x 1002 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 3 (0.0 s)
n=23: 1255 x 1255 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 4 (0.1 s)
n=24: 1575 x 1575 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 4 (0.1 s)
n=25: 1958 x 1958 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 4 (0.1 s)
n=26: 2436 x 2436 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 4 (0.2 s)
n=27: 3010 x 3010 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 5 (0.3 s)
n=28: 3718 x 3718 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 5 (0.4 s)
n=29: 4565 x 4565 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 5 (0.6 s)
n=30: 5604 x 5604 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 5 (0.8 s)
n=31: 6842 x 6842 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 5 (1.1 s)
n=32: 8349 x 8349 pairs; realised <=> rule: True (disagreements 0; rule holds but not realised: 0); primes 6 (1.9 s)
Corollary 5.2 (and its converse) for all pairs of partitions, 3 <= n <= 32: True
