The current issue of Australasian Journal of Combinatorics (vol. 51: 243-257) includes a joint paper by Marlboro College math professor Matt Ollis and his former student Devin Willmott ’11. Titled “On twizzler, zigzag and graceful terraces,” the paper adds to our mathematical knowledge of balanced sequences known as “terraces.”
“There are three somewhat separate problems addressed in the paper, tied together through their use of terraces,” said Matt. “A terrace is a structured pattern that might or might not exist in each of infinitely many mathematical objects called groups. They were originally developed to help with the design of agricultural experiments but have since been found to have applications to other situations and mathematicians also study them in their own right.”
For example, “twizzler terraces”—named by previous authors for the turkey twizzlers found on the menu in some British schools—are terraces that appear to twist in on themselves. In their paper, Matt and Devin classify what types of twizzler terrace can possibly exist and exactly when they do.
“Terraces are combinatorial objects rooted in finite group theory,” said Devin, who collaborated with Matt on this paper as part of his Plan of Concentration at Marlboro on group theory. By leaving behind most of the mathematical rules we are familiar with, collections of elements, or “groups,” are found to interact with each other in new and significant ways. “The ideas behind group theory are fairly unlike any other discipline I have seen, and lead to surprising and unintuitive but elegant results,” Devin said.