The Realization Problem for Discrete Morse Functions on Trees

• 作者: Yuqing Liu Nicholas A.Scoville
• 来源期刊: 代数集刊（英文版）
• 年，卷（期）: 2020,（3）
• 页码范围: 455-468
• 页数: 14页
• 语种: 英文
• DOI: 10.1142/S1005386720000371

摘要

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.Then we 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.This is a version of the "realization problem" of the persistence map.We conclude with an example illustrating our construction.