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Communal Partitions of Integers
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Darren B. Glass
Published/Copyright:
May 31, 2012
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 analogous question counting the number of k-tuples of nonnegative integers none of which is more than 
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.
Received: 2011-06-28
Revised: 2011-08-26
Accepted: 2011-11-22
Published Online: 2012-05-31
Published in Print: 2012-June
© 2012 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- On a Theorem of Prachar Involving Prime Powers
- A Novel Approach to the Discovery of Binary BBP-Type Formulas for Polylogarithm Constants
- A Recurrence Related to the Bell Numbers
- Sum-Product Estimates Applied to Waring's Problem over Finite Fields
- Communal Partitions of Integers
- On Computation of Exact van der Waerden Numbers
- On the Complexity of Chooser–Picker Positional Games
- Partition of an Integer into Distinct Bounded Parts, Identities and Bounds
- A Correlation Identity for Stern's Sequence
- Primitive Prime Divisors in Zero Orbits of Polynomials
