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The jaggedness of an order ideal I in a poset P is the number of maximal elements in I plus the number of minimal elements of P not in I. A probability distribution on the set of order ideals of P is toggle-symmetric if for every p ∈ P, the probability that p is maximal in I equals the probability that p is minimal not in I. In this paper, we prove a… (More)

- Shahrzad Haddadan, Peter Winkler
- STACS
- 2017

Markov chains defined on the set of permutations of 1, 2,. .. , n have been studied widely by mathematicians and theoretical computer scientists [15, 4, 1]. We consider chains in which a position i < n is chosen uniformly at random, and then σ(i) and σ(i+1) are swapped with probability depending on σ(i) and σ(i+1). Our objective is to identify some… (More)

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