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