#### Event Title

#### Description

In this talk, I 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.

#### Date of Event

January 30, 2020

#### Location

Parker Room 338

#### Included in

Soccer Tournament Matrices

Parker Room 338

In this talk, I 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.