P. HISTORY OF ' AATHEMATICAL - School of Mathematics

DETERMINANTS
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side the array. The three determinants which are viewed as "derivational
functions" of this function U are denoted by Cayley KU, FU,
'ifU, symbols which "possess properties which it is the object of this
section to investigate," KU being what later came to be called the
"discriminant" of U.
In the second part of this paper of 1843, Cayley deals (as Muir
explains)! with a class of functions obtainable from the use of m sets
of n indices in the way in which a determinant is obtainable from only
two sets. The general symbol used for such a function is
which stands for the sum of all the different terms of the form ±T' ±.,
±I •••• Ap,l