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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
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Abstract |
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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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Keywords
discrete Morse theory, homological sequence, gradient
vector field, trees, Dyck path
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Mathematical Subject Classification 2010
Primary: 05E45
Secondary: 57M15, 05C05, 68R10
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Milestones
Received: 15 March 2019
Accepted: 5 March 2020
Published: 30 March 2020
Communicated by Colin Adams
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Authors |
| Ian Rand | |
| University of Deleware Newark, DE United States |
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| Nicholas A. Scoville | |
| Mathematics and Computer Science
Department Ursinus College Collegeville, PA United States |
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