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The Ramanujan Journal

, Volume 10, Issue 2, pp 215–235 | Cite as

Jagged Partitions

  • J.-F. Fortin
  • P. Jacob
  • P. Mathieu
Article

Abstract

By jagged partitions we refer to an ordered collection of non-negative integers (n1, n2,..., n m ) with n m p for some positive integer p, further subject to some weakly decreasing conditions that prevent them for being genuine partitions. The case analyzed in greater detail here corresponds to p = 1 and the following conditions n i ni+1−1 and n i ni+2. A number of properties for the corresponding partition function are derived, including rather remarkable congruence relations. An interesting application of jagged partitions concerns the derivation of generating functions for enumerating partitions with special restrictions, a point that is illustrated with various examples.

Keywords

partitions generating functions congruence relations 

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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Département de physique, de génie physique et d'optiqueUniversité LavalQuébecCanada

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