Prime component-preservingly amphicheiral link with odd minimal crossing number

Abstract

For every odd integer $c\ge 21$, we raise an example of a prime component-preservingly amphicheiral link with the minimal crossing number $c$. The link has two components, and consists of an unknot and a knot which is ($-$)-amphicheiral with odd minimal crossing number. We call the latter knot a Stoimenow knot. We also show that the Stoimenow knot is not invertible by the Alexander polynomials.