# From Trees to Barcodes and Back Again II: Combinatorial and Probabilistic Aspects of a Topological Inverse Problem

@inproceedings{Curry2021FromTT, title={From Trees to Barcodes and Back Again II: Combinatorial and Probabilistic Aspects of a Topological Inverse Problem}, author={Justin Curry and Jordan DeSha and Ad'elie Garin and Kathryn Hess and Lida Kanari and Brendan Mallery}, year={2021} }

In this paper we consider two aspects of the inverse problem of how to construct merge trees realizing a given barcode. Much of our investigation exploits a recently discovered connection between the symmetric group and barcodes in general position, based on the simple observation that death order is a permutation of birth order. The first important outcome of our study is a clear combinatorial distinction between the space of phylogenetic trees (as defined by Billera, Holmes and Vogtmann) and… Expand

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