On permutation polytopes - notions of equivalence
classification
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equivalenceequivalentexamplespermutationpolytopesaffinelyansweringapply
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We clarify the notion of effective equivalence and characterize geometrically the effectively equivalent permutation groups. In particular, we present examples showing that the latter do not correspond to affinely equivalent polytopes thereby answering Question 2.12 of [BHNP09]. We apply our characterization to our examples and formulate several questions.
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