Verschiebung and Frobenius operators
Metropolis and Rota introduced the concept of the necklace ring Nr(A) of a commutative ringA. WhenA contains Q as a subring there is a natural bijection γ:Nr(A→1+tA. Grothendieck has introduced a ring structure on 1+tA[t] while studyingK-theoretic Chern classes. Nr(A) comes equipped with two families of operatorsFr,Vr called the Frobenius and Verschiebung operators. Mathematicians studying formal group laws have introduced two families of operators,Fr, andVr on 1+tA[t]. Metropolis and Rota have not however tried to show that γ preserves, these operators. They transport the operators from Nr(A) to 1+tA[t] using γ. In our present paper we show that γ does preserve all these operators.