#### Title of Oral/Poster Presentation

On Tournaments with Non-Integer Weighted Arcs

#### Class

Article

#### College

College of Science

#### Faculty Mentor

David Brown

#### Presentation Type

Poster Presentation

#### Abstract

A tournament matrix is a square 0-1 matrix which satisfies: A+A^T = J-I, where J is the all one's matrix, and I is the identity matrix. A generalized tournament matrix is a non-negative square matrix which satisfies A+A^T = J-I. We define several polytopes within generalized tournament matrices and subsets thereof. Results about extreme values and the polytope are given. In addition, we define an "expected tournament" from a generalized tournament matrix and give results with respect to the polytopes and score sequences of a tournament.

#### Location

The North Atrium

#### Start Date

4-12-2018 3:00 PM

#### End Date

4-12-2018 4:15 PM

On Tournaments with Non-Integer Weighted Arcs

The North Atrium

A tournament matrix is a square 0-1 matrix which satisfies: A+A^T = J-I, where J is the all one's matrix, and I is the identity matrix. A generalized tournament matrix is a non-negative square matrix which satisfies A+A^T = J-I. We define several polytopes within generalized tournament matrices and subsets thereof. Results about extreme values and the polytope are given. In addition, we define an "expected tournament" from a generalized tournament matrix and give results with respect to the polytopes and score sequences of a tournament.