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Prime length necklace colorings · case 03

Dividing all words by the length mishandles constant words with smaller rotation orbits.

Member previewVariant 3 · 3 implementations · 4 checks per implementation

Case contract

Nonnegative integer counts. Permutation and combination counts are zero when a requested selection exceeds the available objects. Shape sizes satisfy the preconditions stated below. length is prime and colors>=1; count colorings of a labelled-position cycle up to rotations, retaining reflection distinctions. Exact operational definition: (colors**length+(length-1)*colors)//length

Why this case matters

Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Combinatorics results depend on the stated convention.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
fixture 1: (3, 2)	`2`	`4`	Failed

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