Choice Functions, Digraphs, and Balanced Allocations
Electronic Theses and Dissertations
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- abstract
- In this thesis, we consider broadly the concept of choice in a variety of settings, focusing on equity in selection. In particular, we introduce the concept of (pair-wise) domination graphs for hypergraphs endowed with a choice function on edges, and are interested, for instance, in minimal numbers of edges for associated domination graphs. Theorems regarding the existence of balanced (zero-edge) domination graphs are presented. In addition, we consider fairness for choice functions, from a sequential perspective, prove existence of fair choice, and consider connections with balanced allocation, path-connected directed graphs and cyclic preference. Several open questions are posed.
- subject
- Choice function
- Digraphs
- Domination
- Fair choice
- Hypergraphs
- Hypertournaments
- contributor
- Berenhaut, Kenneth S. (committee chair)
- Mason, Sarah K. (committee member)
- Gemmer, John (committee member)
- date
- 2017-06-15T08:36:13Z (accessioned)
- 2022-06-01T08:30:12Z (available)
- 2017 (issued)
- degree
- Mathematics and Statistics (discipline)
- embargo
- 2022-06-01 (terms)
- identifier
- http://hdl.handle.net/10339/82247 (uri)
- language
- en (iso)
- publisher
- Wake Forest University
- title
- Choice Functions, Digraphs, and Balanced Allocations
- type
- Thesis