# Combinatorics Seminar 2018

Date: Mon, Oct 08, 2018

Time: 15:00 - 16:00

Venue: Middle Meeting Room

Title: Treasure hunt: mistakes and wrong turnings in the search for good designs

Abstract:

A Latin square of order $n$ can be used to make an incomplete-block design for $n^2$ treatments in $3n$ blocks of size $n$. The cells are the treatments, and each row, column and letter defines a block. Any pair of treatments concur in $0$ or $1$ blocks, and it is known that the block design is optimal for these parameters.

If there are mutually orthogonal Latin squares, then the process can be continued, eventually giving an affine plane. But there are no mutually orthogonal Latin squares of order $6$, so what should we do if we need a design for $36$ treatments in $30$ blocks of size $6$?

I will describe how a series of mistakes and wrong turnings in a different research project led to an answer.

On the way, we meet triple arrays, sesqui-arrays, the Sylvester graph, and semi-Latin squares.

Slides: View slides

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