Halmos College Presents a Talk on Soccer Tournament Matrices

On Thursday, January 30, at 12:35 p.m. Halmos mathematics faculty member Lei Cao, Ph.D. will present a talk titled “Soccer Tournament Matrices”.

In this talk, he will present a combinatorial object, soccer tournament matrices, which is understandable to undergraduate students and gives a taste of combinatorial matrix theory.

Consider a round-robin tournament of n teams in which each team plays every other team exactly once and where ties are allowed. A team scores 3 points for a win, 1 point for a tie, and 0 point for a loss, then each particular result leads to a soccer tournament matrix. Let T(R, 3) denote the class of all soccer tournament matrices with the row sum vector R. In this talk, I will explore some necessary conditions of a vector R, such that T(R, 3) is nonempty with the audience, and then for some R, I will show an algorithm to construct a soccer tournament matrix whose row sum is R.

Halmos College of Natural Sciences and Oceanography department of mathematics hosts the mathematics colloquium series in Parker Building, Room 338. For more information about the math colloquium series, please contact mathematics faculty member Jing Chen, Ph.D. (jchen1@nova.edu) or Evan Haskell (haskell@nova.edu).