The field of topological data analysis seeks to use techniques in topology to study large data sets. The hope is that rather than single quantities that summarize the data, such as mean or standard deviation, information about the data can be learned by studying the overall ``shape” of the data. One way to summarize this data is through a merge tree. Merge trees can be thought of as keeping track of certain clusters of data and determining when they merge together. In this paper, we will study merge trees induced by a discrete Morse function on a tree. Under a suitable notion of equivalence of merge trees, we then count the number of merge trees that can be induced on a star graph.
Johnson, Benjamin, "Merge Trees in Discrete Morse Theory" (2019). Mathematics Summer Fellows. 12.
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Presented during the 21st Annual Summer Fellows Symposium, July 19, 2019 at Ursinus College.