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

Abstract

The expansion of the symmetric determinantis 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.