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Partition of an Integer into Distinct Bounded Parts, Identities and Bounds
-
Mohammadreza Bidar
Published/Copyright:
May 31, 2012
Abstract.
The partition function 
, which denotes the number of
partitions of a positive integer n into distinct parts, has been
the subject of a dozen papers. In this paper, we study this kind of
partition with the additional constraint that the parts are bounded
by a fixed integer. We denote the number of partitions of an integer
n into distinct parts, each 
, by 
. We find a sharp
upper bound for , and more, an infinite series lower bound
for the partition function . In the last section, we exhibit a
group of interesting identities involving that arise from a
combinatorial problem.
Received: 2011-03-15
Accepted: 2012-01-10
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
