Composition of Integers with Bounded Parts

In this note, we consider ordered partitions of integers such that each entry is no more than a fixed portion of the sum. We give a method for constructing all such compositions as well as both an explicit formula and a generating function describing the number of k-tuples whose entries are bounded in this way and sum to a fixed value g. Required Publisher's Statement Original version is available from the publisher at: http://www.integers-ejcnt.org/ This article is available at The Cupola: Scholarship at Gettysburg College: http://cupola.gettysburg.edu/mathfac/30 #A6 INTEGERS 14 (2014) COMPOSITIONS OF INTEGERS WITH BOUNDED PARTS Darren B Glass Department of Mathematics, Gettysburg College, Gettysburg, Pennsylvania [email protected] Received: 4/22/13, Accepted: 12/27/13, Published: 1/22/14 Abstract In this note, we consider ordered partitions of integers such that each entry is no more than a fixed portion of the sum. We give a method for constructing all such compositions as well as both an explicit formula and a generating function describing the number of k-tuples whose entries are bounded in this way and sum to a fixed value g.In this note, we consider ordered partitions of integers such that each entry is no more than a fixed portion of the sum. We give a method for constructing all such compositions as well as both an explicit formula and a generating function describing the number of k-tuples whose entries are bounded in this way and sum to a fixed value g.