Date of Award
2021
Document Type
Dissertation
Publication Status
Version of Record
Submission Date
October 2026
Thesis/Dissertation Advisor [Chair]
Lundberg, Erik
Abstract
An acyclic orientation of a graph is an assignment of a direction to each edge in a way that does not form any directed cycles. Acyclic orientations of a complete bipartite graph are in bijection with a class of matrices called lonesum matrices, which can be uniquely reconstructed from their row and column sums. We utilize this connection and other properties of lonesum matrices to determine an analytic form of the generating function for the length of the longest path in an acyclic orientation on a complete bipartite graph, and then study the distribution of the length of the longest path when the acyclic orientation is random. We use methods of analytic combinatorics, including analytic combinatorics in several variables (ACSV), to determine asymptotics for lonesum matrices and other related classes.
Extent
72 p.
Recommended Citation
Khera, Jessica, "LONESUM MATRICES AND ACYCLIC ORIENTATIONS: ENUMERATION AND ASYMPTOTICS" (2021). Electronic Theses and Dissertations 2020 - Present. 768.
https://digitalcommons.fau.edu/etd_general/768
Identifier
FA00013716
Comments
Includes bibliography.|Dissertation (PhD)--Florida Atlantic University, 2021.|FAU Electronic Theses and Dissertations Collection|Includes bibliography.