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

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.

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

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