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Enumeration of the Partitions of an Integer into Parts of a Specified Number of Different Sizes and Especially Two Sizes
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Nesrine Benyahia Tani

Algiers 3 University

Faculty of Economics and Management Sciences

2 Ahmed Waked Street

Dely Brahim, Algiers

Algeria

Sadek Bouroubi

University of Science and Technology Houari Boumediene

Faculty of Mathematics

P. O. Box 32

16111 El-Alia, Bab-Ezzouar, Algiers

Algeria

**Abstract:**

A partition of a non-negative integer *n* is a way of writing *n* as a
sum of a nondecreasing sequence of parts. The present paper provides
the number of partitions of an integer *n* into parts of a specified
number of different sizes. We establish new formulas for such
partitions with particular interest to the number of partitions of $n$
into parts of two sizes. A geometric application is given at the end of
this paper.

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(Concerned with sequences
A002133
A117955
A117956.)

Received May 4 2010;
revised version received October 3 2010; January 31 2011; February 28 2011.
Published in *Journal of Integer Sequences*, March 25 2011.

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