#### Document Type

Article

#### Publication Date

5-31-2012

#### Department 1

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.

#### Copyright Note

This is the publisher's version of the work. This publication appears in Gettysburg College's institutional repository by permission of the copyright owner for personal use, not for redistribution.

#### DOI

10.1515/integ.2011.111

#### Recommended Citation

Glass, Darren. (2012) Communal Partition of Integers. Integers, 12:3, 405–416.

#### Required Publisher's Statement

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