Cyclotomic factors of necklace polynomials
Cyclotomic factors of necklace polynomials
We observe that the necklace polynomials $M_d(x) = \frac {1}{d}\sum _{e\mid d}\mu (e)x^{d/e}$ are highly reducible over $\mathbb {Q}$ with many cyclotomic factors. Furthermore, the sequence $\Phi _d(x) - 1$ of shifted cyclotomic polynomials exhibits a qua