Vol. 13, No. 2, 2020

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Discrete Morse functions, vector fields, and homological sequences on trees

Ian Rand and Nicholas A. Scoville

Vol. 13 (2020), No. 2, 219–229
Abstract

We construct a discrete Morse function which induces both a specified gradient vector field and homological sequence on a given tree. After reviewing the basics of discrete Morse theory, we provide an algorithm to construct a discrete Morse function on a tree inducing a desired gradient vector field and homological sequence. We prove that our algorithm is correct, and conclude with an example to illustrate its use.

Keywords
discrete Morse theory, homological sequence, gradient vector field, trees, Dyck path
Mathematical Subject Classification 2010
Primary: 05E45
Secondary: 57M15, 05C05, 68R10
Milestones
Received: 15 March 2019
Accepted: 5 March 2020
Published: 30 March 2020

Communicated by Colin Adams
Authors
Ian Rand
University of Deleware
Newark, DE
United States
Nicholas A. Scoville
Mathematics and Computer Science Department
Ursinus College
Collegeville, PA
United States