Abstract
We consider sorting by a queue that can apply a permutation from a given set over its content. This gives us a sorting device \(\mathbb {Q}_{\varSigma }\) corresponding to any shuffling method \(\varSigma \) since every such method is associated with a set of permutations. Two variations of these devices are considered - \(\mathbb {Q}_{\varSigma }^{\prime }\) and \(\mathbb {Q}_{\varSigma }^{\text {pop}}\). These require the entire content of the device to be unloaded after a permutation is applied or unloaded by each pop operation, respectively.
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