Article
Licensed
Unlicensed Requires Authentication

Combinatorics of Integer Partitions in Arithmetic Progression

Published/Copyright: March 19, 2010
Become an author with De Gruyter Brill
Author Information Explore this Subject
Integers
From the journal Volume 10 Issue 1

Abstract

The partitions of a positive integer n in which the parts are in arithmetic progression possess interesting combinatorial properties that distinguish them from other classes of partitions. We exhibit the properties by analyzing partitions with respect to a fixed length of the arithmetic progressions. We also address an open question concerning the number of integers k for which there is a k-partition of n with parts in arithmetic progression.

Keywords.: Partition; arithmetic progression; AP divisor
Received: 2009-02-09
Revised: 2009-11-18
Accepted: 2009-11-24
Published Online: 2010-03-19
Published in Print: 2010-March

© de Gruyter 2010

Articles in the same Issue

  1. Congruences for Hyper m-ary Overpartition Functions
  2. A Note on Fibonacci-Type Polynomials
  3. Non-Regularity of ⌊α + logk n⌋
  4. Lerch's Theorems over Function Fields
  5. On Normal Numbers and Powers of Algebraic Numbers
  6. Volume as a Measure of Approximation for the Jacobi–Perron Algorithm
  7. Combinatorics of Integer Partitions in Arithmetic Progression
  8. Analogues of Jacobi's Two-Square Theorem: An Informal Account
  9. Convolution Identities for Stirling Numbers of the First Kind
  10. Pattern Occurrence in the Dyadic Expansion of Square Root of Two and an Analysis of Pseudorandom Number Generators
  11. Place-Difference-Value Patterns: A Generalization of Generalized Permutation and Word Patterns
  12. A Multivariate Arithmetic Function of Combinatorial and Topological Significance
https://doi.org/10.1515/integ.2010.007
Keywords for this article
Partition; arithmetic progression; AP divisor

Articles in the same Issue

  1. Congruences for Hyper m-ary Overpartition Functions
  2. A Note on Fibonacci-Type Polynomials
  3. Non-Regularity of ⌊α + logk n⌋
  4. Lerch's Theorems over Function Fields
  5. On Normal Numbers and Powers of Algebraic Numbers
  6. Volume as a Measure of Approximation for the Jacobi–Perron Algorithm
  7. Combinatorics of Integer Partitions in Arithmetic Progression
  8. Analogues of Jacobi's Two-Square Theorem: An Informal Account
  9. Convolution Identities for Stirling Numbers of the First Kind
  10. Pattern Occurrence in the Dyadic Expansion of Square Root of Two and an Analysis of Pseudorandom Number Generators
  11. Place-Difference-Value Patterns: A Generalization of Generalized Permutation and Word Patterns
  12. A Multivariate Arithmetic Function of Combinatorial and Topological Significance
Downloaded on 11.4.2026 from https://www.degruyterbrill.com/document/doi/10.1515/integ.2010.007/html
Scroll to top button