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Jagged Partitions

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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.

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Author notes

  1. J.-F. Fortin

    Present address: Department of Physics and Astronomy, Rutgers, The State University of New Jersey, Piscataway, NJ, 08854-8019

  2. P. Jacob

    Present address: Department of Mathematical Sciences, University of Durham, Durham, DH1 3L, UK

Authors and Affiliations

  1. Département de physique, de génie physique et d'optique, Université Laval, Québec, Canada, G1K 7P4

    J.-F. Fortin, P. Jacob & P. Mathieu

Authors
  1. J.-F. Fortin
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  2. P. Jacob
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  3. P. Mathieu
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Correspondence to J.-F. Fortin.

Additional information

2000 Mathematics Subject Classification: Primary—05A15, 05A17, 05A19

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Fortin, JF., Jacob, P. & Mathieu, P. Jagged Partitions. Ramanujan J 10, 215–235 (2005). https://doi.org/10.1007/s11139-005-4848-8

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  • DOI: https://doi.org/10.1007/s11139-005-4848-8

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