Geodesic
A Note on the Compositions of an Integer
Canadian mathematical bulletin, Tome 1 (1958) no. 3, pp. 169-173

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Given an integer n, we define an r-composition of n as follows:An r-composition of n, (t1, ... , tr), is a set of ti where ti ≥ 1 is an integer for i = 1, ... , r such that If r is an integer such that 1 ≤ r ≤ n, we have, obviously, distinct r - compositions of n. 
Narayana, T. V.; Fulton, G. E. A Note on the Compositions of an Integer. Canadian mathematical bulletin, Tome 1 (1958) no. 3, pp. 169-173. doi: 10.4153/CMB-1958-017-3
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