40 citations · 43 across the 6 of their papers we have counts for
6 papers
Generalizations of nets and Latin squares
Brian Curtin
We examine combinatorial structures that generalize -nets, orthogonal arrays, and mutually orthogonal Latin squares. By a reticulation we mean a point set and two collection…
Combinatorial structures connecting Latin squares and bireversible automata
Brian Curtin, Dmytro Savchuk
This paper explores the theory of letter transducers, Mealy automata, and bireversible automata from a combinatorial perspective analogous to the theory of Latin squares. We view t…
Excluded power graphs of groups
Brian Curtin
Let be a set of integers greater than one. The -excluded power graph of a group has vertex set and an edge from to each power of other th…
Terwilliger algebras constructed from Cayley tables of finite Bol loops
Brian Curtin
We describe the Terwilliger algebras of the four-class Latin-square association schemes arising from Cayley tables of Bol loops. We give some necessary conditions involving Terwill…
Edge-maximality of power graphs of finite cyclic groups
Brian Curtin, Gholam Reza Pourgholi
We show that among all finite groups of any given order, the cyclic group of that order has the maximum number of edges in its power graph. Contains corrections to published versio…
A group sum inequality and its application to power graphs
Brian Curtin, Gholam Reza Pourgholi
Let be a finite group of order , and let be the cyclic group of order . We show that , with e…