Laura Johnson

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20232025

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4 papers · 1 filter

math.CO2025

On relative simple Heffter spaces

Laura Johnson, Lorenzo Mella, Anita Pasotti

In this paper, we introduce the concept of a relative Heffter space which simultaneously generalizes those of relative Heffter arrays and Heffter spaces. Given a subgroup $J$ of an…

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

Additive triples in groups of odd prime order

Sophie Huczynska, Jonathan Jedwab, Laura Johnson

Let $p$ be an odd prime. For nontrivial proper subsets $A, B$ of $Z_{p}$ of cardinality $s, t$ , respectively, we count the number $r (A, B, B)$ of additive triples, namely elemen…

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…