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On the Number of Distinct Terms in the Expansion of Symmetric and Skew Determinants

Published online by Cambridge University Press:  31 October 2008

A. C. Aitken
A. C. Aitken
Affiliation:
The Mathematical Institute, 16 Chambers Street, Edinburgh.
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The expansion of the symmetric determinant

is familiar. It is of six terms; but one term, fgh, is duplicated, and so there are five distinct terms. If we ascertain the number un of distinct terms in the expansions of symmetric determinants of increasing order, we find the following sequence of values, for n = 0, 1, 2, …,

where by convention u0 = 1.

Type
Research Article
Information
Edinburgh Mathematical Notes , Volume 34 , January 1944 , pp. 1 - 5
Copyright
Copyright © Edinburgh Mathematical Society 1944