Session 13 of 28 · 17 May 2025 · not recorded

The Powers of Tournament Matrices

Examining matrix representations of tournaments and their powers

This session was not recorded (17 May 2025).

No notes for this session.

Topics on Tournaments

5 May Introduction Basic definitions and fundamental concepts of tournaments ▶ 1 h 08 min notes
6 May Irreducible Tournaments Exploring irreducible tournaments and their properties ▶ 58 min
7 May Strong Tournaments Understanding strong tournaments and their characteristics ▶ 33 min
8 May Cycles in a Tournament Analysis of cycles and their significance in tournaments ▶ 37 min
9 May Strong Subtournaments of a Tournament Examining strong subtournaments and their relationships not recorded
10 May The Distribution of 3-cycles in a Tournament Statistical analysis of 3-cycles in tournament structures not recorded
11 May Transitive Tournaments Exploring transitive tournaments and their unique properties ▶ 41 min
12 May Sets of Consistent Arcs in a Tournament Understanding consistent arc sets and their implications ▶ 1 h 00 min
13 May The Parity of the Number of Spanning Paths of a Tournament Examining parity properties of spanning paths ▶ 1 h 15 min
14 May The Maximum Number of Spanning Paths of a Tournament Analysis of maximum spanning paths in tournament structures not recorded
15 May An Extremal Problem Exploring extremal problems in tournament theory ▶ 1 h 09 min
16 May The Diameter of a Tournament Understanding tournament diameter and its implications ▶ 42 min
17 May The Powers of Tournament Matrices Examining matrix representations of tournaments and their powers not recorded
18 May Scheduling a Tournament Practical applications in tournament scheduling ▶ 1 h 25 min
19 May Ranking the Participants in a Tournament Methods and algorithms for ranking tournament participants ▶ 1 h 03 min
20 May The Minimum Number of Comparisons Necessary to Determine a Transitive Tournament Optimization problems in transitive tournaments not recorded
21 May Universal Tournaments Exploring the concept and properties of universal tournaments ▶ 1 h 02 min
22 May Expressing Oriented Graphs as the Union of Bilevel Graphs Representation theory for oriented graphs in tournaments ▶ 1 h 02 min
23 May Oriented Graphs Induced by Voting Patterns Applications of tournament theory to voting systems ▶ 46 min
24 May Oriented Graphs Induced by Team Comparisons Applications of tournament theory to sports and competitions ▶ 59 min
25 May Criteria for a Score Vector Understanding the mathematical criteria for valid score vectors not recorded
26 May Score Vectors of Generalizations of Tournaments Extending score vector concepts to generalized tournaments ▶ 56 min
27 May The Number of Score Vectors Combinatorial analysis of possible score vectors ▶ 1 h 05 min
28 May The Largest Score in a Tournament Extremal analysis of maximum scores in tournaments ▶ 1 h 32 min
29 May A Reversal Theorem Exploring reversal properties in tournament theory ▶ 1 h 01 min
30 May Tournaments with a Given Automorphism Group Algebraic analysis of tournament symmetries ▶ 52 min
31 May The Group of the Composition of Two Tournaments Understanding compositional properties of tournament groups ▶ 58 min
1 Jun The Maximum Order of the Group of a Tournament Exploring maximum order properties in tournament groups ▶ 42 min