We present a unitary transformation relating two apparently different supersymmetric lattice models in one dimension. The first cite{FS07} describes semionic particles on a 1D ladder, with supersymmetry moving particles between the two legs. The second cite{GFNR15} is a fermionic model with particle-hole symmetry and with supersymmetry creating or annihilating pairs of domain walls. The mapping we display features non-trivial phase factors that generalise the sign factors occurring in the Jordan-Wigner transformation. We dedicate this work to our friend and colleague Bernard Nienhuis, on the occasion of his 65-th birthday.
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