Peter Cameron's homepage

Welcome to my St Andrews homepage. Under construction 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.

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School of Mathematics and Statistics
University of St Andrews
North Haugh
St Andrews, Fife KY16 9SS
SCOTLAND
Tel.: +44 (0)1334 463769
Fax: +44 (0)1334 46 3748
Email: pjc20(at)st-arthurs(dot)ac(dot)uk
  [oops – wrong saint!]





Page revised 12 September 2016

A problem (Agrawal's conjecture)

Let B be a block of a symmetric 2-(v,k,λ) design. Construct a k×(vk) 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 vk, 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.