Minimal stretch factors of orientation-reversing fully-punctured pseudo-Anosov maps

We show that the stretch factor λ(f) of an orientation-reversing fully-punctured pseudo-Anosov map f on a finite-type orientable surface S, with -χ(S) ≥ 4 and having at least two puncture orbits, satisfies the inequality λ(f)-χ(S) ≥ σ², where σ=1+√2 is the silver ratio. We provide examples showing that this bound is asymptotically sharp. This extends previous results of Hironaka and the third author to orientation-reversing maps.