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Macaulay Expansion

B. Sury
The American Mathematical Monthly
Vol. 121, No. 4 (April 2014), pp. 359-360
DOI: 10.4169/amer.math.monthly.121.04.359
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.121.04.359
Page Count: 2
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Abstract

Abstract Given natural numbers n and r, the “greedy” algorithm enables us to obtain an expansion of the integer n as a sum of binomial coefficients in the form \documentclass{article} \pagestyle{empty}\begin{document} ${a_r \choose r} + {a_{r-1} \choose r-1} + \cdots + {a_1 \choose 1}$ \end{document} . We give an alternate interpretation of this expansion, which also proves its uniqueness in an interesting manner.