Jeffrey Dinitz, professor of mathematics and statistics, will give a University Scholar Seminar, "Thinking Deeply about Putting Numbers in Boxes," Wednesday, April 15 at 4 p.m. in Memorial Lounge, Waterman Building.

You are the commissioner of a neighborhood football league. Your task: organize a round-robin tournament so that the Aardvarks, Bumblebees, Clams, and Dromedaries all play each other. It's just four teams. Not too hard, right? In round one it's A vs B and C vs D. Round two: A vs C and B vs D. Round three: A vs D and C vs B. All set to play ball?

Wait, I forgot to tell you a few things.

Actually, the teams have to play each other three times, at least once at North Field and once in South Field. And they also need to play the crosstown league Pipsqueeks, Tiny Tots, Pencil Necks and Flyweights so that every team plays each other once, and no team plays on the other side of town more than twice.

Pencil getting dull? You could keep scratching away.

Or you could consult mathematician Jeffrey Dinitz. That's what the XFL Professional Football League did.

Dinitz will be telling this story, and others from his career in mathematics, during a University Scholar seminar on "Thinking Deeply about Putting Numbers in Boxes," Wednesday, April 15 at 4 p.m. in Memorial Lounge, Waterman Building.

The lecture is free and open to the public. "This will not be a technical talk," Dinitz says, "I'll make the mathematics understandable to a general audience."

Sudoku, drugs, football

Dinitz will speak about his life's work as a leading scholar of combinatorial design theory. Which, in 2000, lead the commissioner of the ill-fated XFL league to hire him and his partner to sort out their league schedule.

"Actually I'm not a guy who usually goes around making round-robin tournaments," Dinitz says, laughing, "but I do make combinatorial objects that may have applications to real tournaments, and I did do this one for the XFL."

Unfortunately, the league failed, but not Dinitz's mathematics. "The commissioner of the league said that 'people complained about everything but your schedule,'" Dinitz says. "'It was the only thing right with the whole league,' the commissioner said."

Tournaments are one application of combinatorial design theory. Others abound: the now wildly popular logic game Sudoku, experimental design (e.g., a drug company wants to optimize how to give eight different drugs in pairs and triplets to 1,000 rats), forms of geometric art, and even some orchestral music.

Deeps numbers in boxes

Underlying these applications is a rich area of mathematical theory that includes structures like Latin Squares, strange patterns like the "combinatorial explosion," and solutions to perplexing questions like "Kirkman's Schoolgirl Problem," in which "fifteen young ladies in a school walk out three abreast for seven days in succession," Thomas Kirkman wrote in 1850, and "it is required to arrange them daily so that no two shall walk twice abreast."

Dinitz will also speak about his own maddeningly simple — but difficult to prove — "Dinitz Conjecture." (More on the conjecture on Wikipedia, or hear about it from the conjecturing mathematician himself at the lecture.)

"My work is putting numbers in boxes," Dinitz says, "and then thinking deeply about what they mean."