II. Second memoir on the compositions of numbers

Abstract

In a Memoir on the Theory of the Compositions of Numbers, read before the Royal Society, November 24, 1892, and published in the ‘Philosophical Transactions’ for 1893, I discussed the compositions of multipartite numbers by a graphical method. The generating function produced by the method was of the form 1/1-∑α 1 + (1 - λ) ∑α 1 α 2 - (1 - λ) 2 ∑α 1 α 2 α 3 + . . . . , a symmetrical function of the quantities α. The investigation of the present paper leads, in part, to the same generating function which is subjected to a close examination. Moreover, the whole research has to do with the compositions of numbers, and appropriately follows the Memoir of 1893.