Damir Yeliussizov

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Merge trees represent the topology of scalar functions. To assess the topo-logical similarity of functions, one can compare their merge trees. To do so, one needs a notion of a distance between merge trees, which we define. We provide examples of using our merge tree distance and compare this new measure to other ways used to characterize topological(More)
Catalan numbers arise in many enumerative contexts as the counting sequence of combinatorial structures. In this work, we consider natural Markov chains on some of the realizations of the Catalan sequence. While our main result is in deriving an O(n 2 log n) bound on the mixing time in L2 (and hence total variation) distance for the random transposition(More)
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