Submission Date

7-20-2018

Document Type

Paper

Department

Mathematics

Faculty Mentor

Nicholas Scoville

Comments

Presented during the 20th Annual Summer Fellows Symposium, July 20, 2018 at Ursinus College.

Project Description

We introduce a new notion of equivalence of discrete Morse functions on graphs called persistence equivalence. Two functions are considered persistence equivalent if and only if they induce the same persistence diagram. We compare this notion of equivalence to other notions of equivalent discrete Morse functions. We then compute an upper bound for the number of persistence equivalent discrete Morse functions on a fixed graph and show that this upper bound is sharp in the case where our graph is a tree. We conclude with an example illustrating our construction.

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