# 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.