• Corpus ID: 251564644

Perfect shuffling with fewer lazy transpositions

  title={Perfect shuffling with fewer lazy transpositions},
  author={Carla Groenland and Tom Johnston and Jamie Radcliffe and Alex D. Scott},
A lazy transposition ( a, b, p ) is the random permutation that equals the identity with probability 1 − p and the transposition ( a, b ) ∈ S n with probability p . How long must a sequence of independent lazy transpositions be if their composition is uniformly distributed? It is known that there are sequences of length (cid:0) n 2 (cid:1) , but are there shorter sequences? This was raised by Fitzsimons in 2011, and independently by Angel and Holroyd in 2018. We answer this question negatively… 

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