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

Rand, Ian; Scoville, Nicholas A.

doi:10.2140/involve.2020.13.219

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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

DOI: 10.2140/involve.2020.13.219

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

Vol. 13, No. 2, 2020