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- W2912694889 abstract "In this paper we study functions on the interval that have the same persistent homology, which is what we mean by the fiber of the persistence map. By imposing an equivalence relation called graph-equivalence, the fiber of the persistence map becomes finite and a precise enumeration is given. Graph-equivalence classes are indexed by chiral merge trees, which are binary merge trees where a left-right ordering of the children of each vertex is given. Enumeration of merge trees and chiral merge trees with the same persistence makes essential use of the Elder Rule, which is given its first detailed proof in this paper." @default.
- W2912694889 created "2019-02-21" @default.
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- W2912694889 date "2018-12-01" @default.
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- W2912694889 title "The fiber of the persistence map for functions on the interval" @default.
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- W2912694889 doi "https://doi.org/10.1007/s41468-019-00024-z" @default.
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