R. J. R. Abel

activity

20152024

collaborators

4 papers

math.CO2024

Improvements for lower bounds of mutually orthogonal Latin squares of sizes $54$ , $96$ and $108$

R. Julian R. Abel, Ingo Janiszczak, Reiner Staszewski

We will show that there are at least 8, 10 and 9 mutually orthogonal Latin squares (MOLS) of orders $n = 54$ , $96$ and $108$ . The cases $n = 54$ and $96$ are obtained by constructing s…

math.CO2024

Direct constructions of some group divisible designs with block size $4$ and up to $50$ points

R. Julian. R. Abel, Thomas Britz, Yudhistira A. Bunjamin +1

In this note, we give direct constructions of some group divisible designs (GDDs) with block size $4$ that have up to $50$ points.

math.CO2023

Group divisible designs with block size 4 and group sizes 4 and 7

R. Julian R. Abel, Thomas Britz, Yudhistira A. Bunjamin +1

In this paper, we consider the existence of group divisible designs (GDDs) with block size $4$ and group sizes $4$ and $7$ . We show that there exists a 4-GDD of type $4^{t} 7^{s}$ for…

math.CO2015

On generalized Howell designs with block size three

R. Julian R. Abel, Robert F. Bailey, Andrea C. Burgess +2

In this paper, we examine a class of doubly resolvable combinatorial objects. Let $t, k, λ, s$ and $v$ be nonnegative integers, and let $X$ be a set of $v$ symbols. A generalized H…

Improvements for lower bounds of mutually orthogonal Latin squares of sizes 54, 96 and 108

Direct constructions of some group divisible designs with block size 4 and up to 50 points

Group divisible designs with block size 4 and group sizes 4 and 7

On generalized Howell designs with block size three

Improvements for lower bounds of mutually orthogonal Latin squares of sizes $54$ , $96$ and $108$

Direct constructions of some group divisible designs with block size $4$ and up to $50$ points