Some Methods applicable to Identities and Inequalities of Symmetric Algebraic Functions of n Letters

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Abstract
The methods explained here are applicable to a large number of problems relating to the symmetric algebraic functions of n letters, and the special results here deduced from them are merely specimens to indicate some of the ways of applying these methods.In the first section the main principle adopted is that of taking the standard form of a symmetric function to be a sum extending over all the cases of the typical term got by permuting the letters involved in all possible ways, whether they are different or not; and the main result reached is an Inequality Theorem arrived at by expressing the excess of the greater over the less in an explicitly positive form.

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