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An integer n may be partitioned into the set of integers (α1, α2, …, αl), where 
Whenever αi−1>αi the substitution of αi+1 for αi, where αi may be αi+1≡0, would give a partition of n+1 whilst the substitution of αi−1—1 for αi−1 would give a partition of n—1; partitions of n+1 and of n—1 so arising will be said to be associated with the given partition of n.
That the determinant
where hr is the rth complete homogeneous symmetric function in a set of n arguments, is equal to the quotient of a particular pair of alternants was shown essentially by Jacobi in 1841 and by Trudi in 1864. The present note exhinits this well-know relation, (3), as the immediate consequence of a simple matrix equality.
