Perfect 1-Factorisations and Hamiltonian Latin Squares

Explore a 29-minute conference talk by Ian Wanless from Monash University on perfect 1-factorisations and Hamiltonian Latin squares. Delve into topics such as Kotzig's conjecture, enumeration of sporadic orders, Beck's Theorem, and solving Falconer's problem. Learn about quadratic orthomorphisms, quasigroups, and varieties as part of the "Stinson66 - New Advances in Designs, Codes and Cryptography" series at the Fields Institute. Gain insights into the connections between 1-factorisations and Latin squares, and discover the latest developments in this fascinating area of mathematics.

Syllabus

Intro
The cast
A perfect 1-factorisation of Ks
1-factorisations from Latin squares
Kotzig's conjecture
Enumeration
78 Sporadic Orders of P1Fs of K
Conjugates of LS
Use a quadratic orthomorphism!
Beck's Theorem
Example p= 11
Phase 2
The end game
Not atomic
Quasigroups
Varieties
Solving Falconer's problem
Loose ends
Other families?
Happy 66 Doug