Title: Reconstructing a Lattice Equation: a Non-Autonomous Approach to the Hietarinta Equation,
Abstract: In this paper we construct a non-autonomous version of the Hietarinta
equation [Hietarinta J., J. Phys. A: Math. Gen. 37 (2004), L67-L73] and study
its integrability properties. We show that this equation possess linear growth
of the degrees of iterates, generalized symmetries depending on arbitrary
functions, and that it is Darboux integrable. We use the first integrals to
provide a general solution of this equation. In particular we show that this
equation is a sub-case of the non-autonomous $Q_{\rm V}$ equation, and we
provide a non-autonomous Möbius transformation to another equation found in
[Hietarinta J., J. Nonlinear Math. Phys. 12 (2005), suppl. 2, 223-230] and
appearing also in Boll's classification [Boll R., Ph.D. Thesis, Technische
Universität Berlin, 2012].