M. Ollis

activity

20162025

most citedTerraces for Small Groups

3 citations · 8 across the 13 of their papers we have counts for

collaborators

15 papers

math.CO2025

A Discrete Logarithm Construction for Orthogonal Double Covers of the Complete Graph by Hamiltonian Paths

M. A. Ollis

During their investigation of power-sequence terraces, Anderson and Preece briefly mention a construction of a terrace for the cyclic group $Z_{n}$ when $n$ is odd and $2n+1…

math.CO2025

Construction Techniques for Linear Realizations of Multisets with Small Support

Onur Ağırseven, M. A. Ollis

A Hamiltonian path in the complete graph $K_{v}$ whose vertices are labeled with the integers $0, 1, \dots, v - 1$ is a linear realization for the multiset $L$ of the linear edge-lengths…

math.CO2025

A Coprime Buratti-Horak-Rosa Conjecture and Grid-Based Linear Realizations

Onur Agirseven, M. A. Ollis

We propose a "Coprime Buratti-Horak-Rosa (BHR) Conjecture": If $L$ is a multiset of size $v - 1$ with support contained in ${1, 2, \dots, ⌊ v /2 ⌋}$ such that $\gcd(v,x…

math.CO2024

Grid-Based Graphs, Linear Realizations and the Buratti-Horak-Rosa Conjecture

Onur Agirseven, M. A. Ollis

Label the vertices of the complete graph $K_{v}$ with the integers ${0, 1, \dots, v - 1}$ and define the {\em length} $ℓ$ of the edge between distinct vertices labeled $x$ and $y…

math.CO2023★ 1 cited

A Comment on Dean's Construction of Prime Labelings on Ladders

Stephen J. Curran, M. A. Ollis

A prime labeling on a graph of order $m$ is an assignment of ${1, 2, \dots, m}$ to the vertices of the graph such that each pair of adjacent vertices has coprime labels. The l…

math.CO2023

Sequencings in Semidirect Products via the Polynomial Method

Simone Costa, Stefano Della Fiore, M. A. Ollis

The partial sums of a sequence $x = x_{1}, x_{2}, \dots, x_{k}$ of distinct non-identity elements of a group $(G, \cdot)$ are $s_{0} = i d_{G}$ and $s_{j} = \prod_{i = 1}^{j} x_{i}$ for $0…

math.CO2022

On Sequences in Cyclic Groups with Distinct Partial Sums

Simone Costa, Stefano Della Fiore, M. A. Ollis +1

A subset of an abelian group is {\em sequenceable} if there is an ordering $(x_{1}, \dots, x_{k})$ of its elements such that the partial sums $(y_{0}, y_{1}, \dots, y_{k})$ , given by $y_0…

math.CO2022★ 1 cited

The Buratti-Horak-Rosa Conjecture Holds for Some Underlying Sets of Size Three

Pranit Chand, M. A. Ollis

The Buratti-Horak-Rosa Conjecture concerns the possible multisets of edge-labels of a Hamiltonian path in the complete graph with vertex labels $0, 1, \dots, v - 1$ under a partic…

math.CO2021

Growable Realizations: a Powerful Approach to the Buratti-Horak-Rosa Conjecture

M. A. Ollis, Anita Pasotti, Marco A. Pellegrini +1

Label the vertices of the complete graph $K_{v}$ with the integers ${0, 1, \dots, v - 1}$ and define the length of the edge between $x$ and $y$ to be $min (∣ x - y ∣, v - ∣ x - y ∣)$ .…

math.CO2019

Roman and Vatican Crossover Designs

M. A. Ollis

Latin squares with a balance property among adjacent pairs of symbols---being "Roman" or "row-complete"---have long been used as uniform crossover designs with the number of treatm…

math.CO2019★ 3 cited

Sequences in Dihedral Groups with Distinct Partial Products

M. A. Ollis

Given a subset $S$ of the non-identity elements of the dihedral group of order $2 m$ , is it possible to order the elements of $S$ so that the partial products are distinct? This is…

math.CO2018

The spectrum of group-based Latin squares

M. A. Ollis, Christopher R. Tripp

We construct sequencings for many groups that are a semi-direct product of an odd-order abelian group and a cyclic group of odd prime order. It follows from these constructions tha…

math.CO2018

Distinct Partial Sums in Cyclic Groups: Polynomial Method and Constructive Approaches

Jacob Hicks, M. A. Ollis, John. R. Schmitt

Let $(G, +)$ be an abelian group and consider a subset $A \subseteq G$ with $∣ A ∣ = k$ . Given an ordering $(a_{1}, \dots, a_{k})$ of the elements of $A$ , define its {\em partial sums} by…

math.CO2018

Infinite Latin Squares: Neighbor Balance and Orthogonality

Anthony B. Evans, Gage N. Martin, Kaethe Minden +1

Regarding neighbor balance, we consider natural generalizations of $D$ -complete Latin squares and Vatican squares from the finite to the infinite. We show that if $G$ is an infinit…

math.CO2016★ 3 cited

Terraces for Small Groups

M. A. Ollis

We use heuristic algorithms to find terraces for small groups. We show that Bailey's Conjecture (that all groups other than the non-cyclic elementary abelian 2-groups are terraced)…