Flavour-changing neutral-current interactions of the top quark can be searched for in top-quark pair production with one top quark decaying to an up-type quark and a neutral boson, and they can be searched for in the single production of a top quark in association with such a boson. Both processes interfere if an additional up-type quark is produced in the case of single production. The impact of these interference effects on searches for flavour-changing neutral currents at the LHC is studied for the case where the neutral boson is a photon or a $Z$ boson. Interference effects are found to be smaller than variations of the renormalisation and factorisation scales.
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