XVI. Memoir on the theory of the partition of numbers.—Part I

Abstract

Art. 1. I have under consideration multipartite numbers as defined in a former paper. I recall that the multipartite number ᾱβ̄γ̄ . . . , may be regarded as specifying α + β + γ . . . things, α of one sort, β of a second, γ of a third, and so forth. If the things be of m different sorts the number is said to be multipartite of order m or briefly an m -partite number. It is convenient to call α , β , γ , . . . the first, second, third . . . figures of the multipartite number. If such a number be divided into parts each part is regarded as being m -partite; if the order in which the parts are written from left to right is essential we obtain a composition of the multipartite number; whereas if the parts themselves are alone specified, and not the order of arrangement, we have a partition of the multipartite number. This, and much more, is explained in the paper quoted, which is concerned only with the compositions of multipartite numbers.