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.