check_note.py
PART (i): LR coefficients by skew Kostka numbers and the inverse Kostka matrix; brute force, n <= 12
  pairs mu in lambda (0 < |mu| < |lambda| <= 12): 8312; nonzero coefficients: 20237; 0.2 s
  (largest c^lambda_{mu,nu*} seen: 1)
  cases (n,k,d), 2 <= n <= 12, 1 <= k <= n-1, 1 <= d <= n: 572
  cases without a merged optimum (max Delta, merged max): [(10, 5, 5, 72, 70), (12, 5, 6, 102, 100), (12, 7, 6, 102, 100)]
  part (i) done, 0.5 s
PART (ii): optimal triples of Corollary D and the construction of Theorem A, n <= 12
  cases (n,k,d), 2 <= d <= n: 506; triples checked: 575; cases in which every maximizer of the form of Theorem B has shape B: 3; 0.0 s
PART (iii): Theorem C against the maximization of Theorem A, 2 <= n <= 30, 1 <= k <= n-1, 2 <= d <= n
  cases: 8555; 2.4 s
  plain and O(1) candidate lists agree, count bound, d >= n (n <= 16); 2.6 s
PART (iv): Proposition 6.4, Proposition 7.1, examples, Table 1
  cases without a merged optimum (k <= n/2, 2 <= d <= n): 24 with n <= 20, 141 with n <= 30
  part (iv) done, 1.0 s
PART (v): the displayed formulas of Jakab-Solymos-Zimboras (Section 1.3)
  cases 3 <= n <= 20, 1 <= k <= n/2, 2 <= d <= n-1: 1185
  eq. (13), all heights, exact Delta: differs in 24
  eq. (16), exact Delta: differs in {'printed, ties down': 956, 'printed, ties up': 943, 'centre d n_A/n, ties down': 24, 'centre d n_A/n, ties up': 24}
  eq. (15) with (16):    differs in {'printed, ties down': 956, 'printed, ties up': 947, 'centre d n_A/n, ties down': 249, 'centre d n_A/n, ties up': 251}
  eq. (15) vs merged balanced pair, n <= 40: 149530 quadruples; differs in 11753 as printed, in 0 with + instead of -
  eq. (11): maximum over (mu, nu) equals the exact value in all 1285 cases n <= 20, k <= n/2, 2 <= d <= n
  part (v) done, 3.3 s
PART (vi): all configurations, 2 <= d <= n <= 9 (Lemma 5.2, Lemma 5.4, Theorem B, Theorem C)
  cases: 204; configurations: 10737; 0.1 s
checks per part: (i) 159691, (ii) 2093, (iii) 13355, (iv) 296664, (v) 12014, (vi) 11349
TOTAL checks: 495166
TOTAL failures: 0
running time: 7 s
