Document Type

Article

Publication Date

5-31-2012

Department

Mathematics

Abstract

There is a well-known formula due to Andrews that counts the number of incongruent triangles with integer sides and a fixed perimeter. In this note, we consider the analagous question counting the number of k-tuples of nonnegative integers none of which is more than 1/(k−1) of the sum of all the integers. We give an explicit function for the generating function which counts these k-tuples in the case where they are ordered, unordered, or partially ordered. Finally, we discuss the application to algebraic geometry which motivated this question.

Required Publisher's Statement

The original version is available from the publisher at: http://www.westga.edu/~integers/cgi-bin/get.cgi

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