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A combinatorial proof of symmetry among minimal star factorizations (1109.4642v2)
Published 21 Sep 2011 in math.CO
Abstract: The number of minimal transitive star factorizations of a permutation was shown by Irving and Rattan to depend only on the conjugacy class of the permutation, a surprising result given that the pivot plays a very particular role in such factorizations. Here, we explain this symmetry and provide a bijection between minimal transitive star factorizations of a permutation \pi having pivot k and those having pivot k'.
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