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On the clique number of Paley graphs and generalized Paley graphs Yip, Chi Hoi
Abstract
Finding reasonably good upper and lower bounds for the clique number of Paley graphs and generalized Paley graphs is an old and open problem in additive combinatorics. In this thesis, we use polynomial methods, together with various tools from number theory, graph theory, and combinatorics, to study this problem. Specifically, we obtain improved upper bounds on the clique number of Paley graphs and generalized Paley graphs over a finite field. We also obtain new upper bounds on the number of distinct roots of lacunary polynomials and improve lower bounds on the number of directions determined by a Cartesian product in an affine Galois plane over a finite field.
Item Metadata
| Title |
On the clique number of Paley graphs and generalized Paley graphs
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| Creator | |
| Publisher |
University of British Columbia
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| Date Issued |
2021
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| Description |
Finding reasonably good upper and lower bounds for the clique number of Paley graphs and generalized Paley graphs is an old and open problem in additive combinatorics. In this thesis, we use polynomial methods, together with various tools from number theory, graph theory, and combinatorics, to study this problem. Specifically, we obtain improved upper bounds on the clique number of Paley graphs and generalized Paley graphs over a finite field. We also obtain new upper bounds on the number of distinct roots of lacunary polynomials and improve lower bounds on the number of directions determined by a Cartesian product in an affine Galois plane over a finite field.
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| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2021-01-07
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0395514
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Graduation Date |
2021-05
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| Campus | |
| Scholarly Level |
Graduate
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| Rights URI | |
| Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International