John B. Polhill

activity

20232025

collaborators

3 papers

math.CO2025

Strongly Regular Graphs with Generalized Denniston and Dual Generalized Denniston Parameters

Shuxing Li, James A. Davis, Sophie Huczynska +2

We construct two families of strongly regular Cayley graphs, or equivalently, partial difference sets, based on elementary abelian groups. The parameters of these two families are…

math.CO2024

Combinatorial transfer: a new method for constructing infinite families of nonabelian difference sets, partial difference sets, and relative difference sets

Eric Swartz, James A. Davis, John Polhill +1

For nearly a century, mathematicians have been developing techniques for constructing abelian automorphism groups of combinatorial objects, and, conversely, constructing combinator…

math.CO2023

Denniston partial difference sets exist in the odd prime case

James A. Davis, Sophie Huczynska, Laura Johnson +1

Denniston constructed partial difference sets (PDSs) with the parameters $(2^{3 m}, (2^{m + r} - 2^{m} + 2^{r}) (2^{m} - 1), 2^{m} - 2^{r} + (2^{m + r} - 2^{m} + 2^{r}) (2^{r} - 2), (2^{m + r} - 2^{m} + 2^{r}) (2^{r} - 1))$ in ele…