Laura Johnson

activity

20232025

collaborators

6 papers

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.NT2024

Beyond uniform cyclotomy

Sophie Huczynska, Laura Johnson, Maura B. Paterson

Cyclotomy, the study of cyclotomic classes and cyclotomic numbers, is an area of number theory first studied by Gauss. It has natural applications in discrete mathematics and infor…

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…

math.CO2023

New constructions for disjoint partial difference families and external partial difference families

S. Huczynska, L. M. Johnson

Recently, new combinatorial structures called disjoint partial difference families (DPDFs) and external partial difference families (EPDFs) were introduced, which simultaneously ge…