XVII. Memoir on the theory of the compositions of numbers
Open Access
- 31 December 1893
- journal article
- Published by The Royal Society in Philosophical Transactions of the Royal Society of London. (A.)
- Vol. 184, 835-901
- https://doi.org/10.1098/rsta.1893.0017
Abstract
1. Compositions are merely partitions in which the order of occurrence of the parts is essential; thus, while the partitions of the number 3 are (3), (21), (12), (111). The enumerations of the compositions of a number n into p parts, zeros excluded, is given by the coefficient of x n in the expansion of ( x + x 2 + x 3 + . . .) p ; this expression may be written ( x /1- x ) p , and the coefficient of x n is seen to be ( n -1 p -1).Keywords
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