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.

DOI

10.1515/integ.2011.111

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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