Welcome to my St Andrews homepage. This page is under construction (and probably always will be!)
I am a half-time Professor in the School of Mathematics and Statistics at the University of St Andrews, and an Emeritus Professor of Mathematics at Queen Mary, University of London.
On this site
School of Mathematics and Statistics
University of St Andrews
St Andrews, Fife KY16 9SS
Tel.: +44 (0)1334 463769
Fax: +44 (0)1334 46 3748
[oops – wrong saint!]
Page revised 12 September 2016
Let B be a block of a symmetric 2-(v,k,λ) design. Construct a k×(v−k) array as follows: first label the blocks different from B with the numbers 1,…, v−1. The rows of the array are indexed by the points of B and the columns by the points outside B. In the cell in row p and column q, we put the labels of the blocks which contain q but not p. Thus each entry is a set of size k−λ; the union of the entries in a row has size v−k, while the union of the entries in a column has size k.
The problem is to produce a new array with a single entry in each cell, that entry being chosen from the set in that position in the first array, in such a way that the entries in any row, and the entries in any column, are all distinct.
It is known that this is impossible for the Fano plane.
Conjecture: The construction above is possible in all other cases.
Old problems are kept here.