n=8 correct input: equals brute force True, fails {'rowsum': 0, 'range': 0}, orth True
  (1) eps flipped for (4, 2, 1, 1): equals brute False, fails {'rowsum': 0, 'range': 0}, orth True
  (2) P+2 for (4, 2, 1, 1): equals brute False, fails {'rowsum': 0, 'range': 3}, orth False
  (1) eps flipped for (3, 3, 2): equals brute False, fails {'rowsum': 0, 'range': 0}, orth True
  (2) P+2 for (3, 3, 2): equals brute False, fails {'rowsum': 0, 'range': 8}, orth False
n=9 correct input: equals brute force True, fails {'rowsum': 0, 'range': 0}, orth True
  (1) eps flipped for (5, 1, 1, 1, 1): equals brute False, fails {'rowsum': 0, 'range': 0}, orth True
  (2) P+2 for (5, 1, 1, 1, 1): equals brute False, fails {'rowsum': 0, 'range': 6}, orth False
  (1) eps flipped for (3, 3, 3): equals brute False, fails {'rowsum': 0, 'range': 0}, orth True
  (2) P+2 for (3, 3, 3): equals brute False, fails {'rowsum': 0, 'range': 9}, orth False
n=10 correct input: equals brute force True, fails {'rowsum': 0, 'range': 0}, orth True
  (1) eps flipped for (5, 2, 1, 1, 1): equals brute False, fails {'rowsum': 0, 'range': 0}, orth True
  (2) P+2 for (5, 2, 1, 1, 1): equals brute False, fails {'rowsum': 0, 'range': 6}, orth False
  (1) eps flipped for (4, 3, 2, 1): equals brute False, fails {'rowsum': 0, 'range': 2}, orth True
  (2) P+2 for (4, 3, 2, 1): equals brute False, fails {'rowsum': 0, 'range': 6}, orth False
(3) n=9 S_n table with one entry +1: column orthogonality holds? False
(3) n=10 S_n table with one entry +1: column orthogonality holds? False
(4) n=10: matching re-check rejects the old matching after deleting one of its edges: 24/24
(5a) A_4: classes C with no perfect matching: [((3, 1), 1), ((3, 1), -1)]
(5b) S_5: classes C for which S_n is NOT expansive (no perfect matching): [(4, 1), (3, 2), (2, 1, 1, 1)]
(5b) S_6: classes C for which S_n is NOT expansive (no perfect matching): [(6,), (4, 1, 1), (3, 2, 1), (2, 2, 2), (2, 1, 1, 1, 1)]
(5b) S_7: classes C for which S_n is NOT expansive (no perfect matching): [(6, 1), (5, 2), (4, 3), (4, 1, 1, 1), (3, 2, 1, 1), (2, 2, 2, 1), (2, 1, 1, 1, 1, 1)]
(5b) S_8: classes C for which S_n is NOT expansive (no perfect matching): [(8,), (6, 1, 1), (5, 2, 1), (4, 3, 1), (4, 2, 2), (4, 1, 1, 1, 1), (3, 3, 2), (3, 2, 1, 1, 1), (2, 2, 2, 1, 1), (2, 1, 1, 1, 1, 1, 1)]
(5b) S_9: classes C for which S_n is NOT expansive (no perfect matching): [(8, 1), (7, 2), (6, 3), (6, 1, 1, 1), (5, 4), (5, 2, 1, 1), (4, 3, 1, 1), (4, 2, 2, 1), (4, 1, 1, 1, 1, 1), (3, 3, 2, 1), (3, 2, 2, 2), (3, 2, 1, 1, 1, 1), (2, 2, 2, 1, 1, 1), (2, 1, 1, 1, 1, 1, 1, 1)]
(5b) S_10: classes C for which S_n is NOT expansive (no perfect matching): [(10,), (8, 1, 1), (7, 2, 1), (6, 3, 1), (6, 2, 2), (6, 1, 1, 1, 1), (5, 4, 1), (5, 3, 2), (5, 2, 1, 1, 1), (4, 4, 2), (4, 3, 3), (4, 3, 1, 1, 1), (4, 2, 2, 1, 1), (4, 1, 1, 1, 1, 1, 1), (3, 3, 2, 1, 1), (3, 2, 2, 2, 1), (3, 2, 1, 1, 1, 1, 1), (2, 2, 2, 2, 2), (2, 2, 2, 1, 1, 1, 1), (2, 1, 1, 1, 1, 1, 1, 1, 1)]
