The isoperimetric and Kazhdan constants associated to a Paley graph
| Autor: | Kevin Cramer, Mike Krebs, Nicole Shabazi, Edward Voskanian, Anthony Shaheen |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Group (mathematics)
Paley graph General Mathematics Modulo 010102 general mathematics 01 natural sciences Upper and lower bounds Combinatorics Kazhdan constant Generating set of a group isoperimetric constant 0101 mathematics Isoperimetric inequality Mathematics::Representation Theory Constant (mathematics) expansion constant 05C99 Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Involve 9, no. 2 (2016), 293-306 |
| ISSN: | 1944-4184 1944-4176 |
| DOI: | 10.2140/involve.2016.9.293 |
| Popis: | In this paper, we investigate the isoperimetric constant (or expansion constant) of a Paley graph, and the Kazhdan constant of the group and generating set associated with a Paley graph. ¶ We give two new upper bounds for the isoperimetric constant [math] for the Paley graph [math] . These bounds improve previously known eigenvalue bounds on [math] . Along with a known eigenvalue lower bound for [math] , they provide a narrow strip in which [math] must live. More precisely, we show that [math] , which implies that [math] . ¶ In addition, we show that the Kazhdan constant associated with the integers modulo [math] and the generating set for the Paley graph [math] approaches [math] as [math] tends to infinity, which is the best possible limit that the Kazhdan constant can be. |
| Databáze: | OpenAIRE |
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