Given a finite-type surface S, it is still unknown exactly which numbers occur as stretch factors of pseudo-Anosov maps on S. It appears there is more flexibility in producing a homeomorphism with a given stretch factor if we allow for the surface to be infinite-type. I’ll discuss current work with Marissa Loving and Chenxi Wu showing every weak Perron number is the stretch factor of some end-periodic homeomorphism on some infinite-type surface.