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