Bijective proofs involving chromatic overpartitions

Mateus Alegri
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 1, Pages 128—136
DOI: 10.7546/nntdm.2019.25.1.128-136
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Authors and affiliations

Mateus Alegri
Department of Mathematics (DMAI), University of Sergipe
49500-000, Itabaiana-SE, Brazil

Abstract

In this paper, our aim is to provide two bijective proofs for identities involving what we call chromatic overpartitions, which is a generalization of the well-known overpartitions class. For this purpose we will give the mathematical definitions of chromatic overpartitions, providing their respective generating functions.

Keywords

  • Integer partitions
  • Overpartitions
  • Chromatic partitions
  • Partition identities

2010 Mathematics Subject Classification

  • Primary
    • 05A17
  • Secondary
    • 11P82
    • 11P84

References

  1. Alegri, M. Combinatorial Interpretations for Identities involving Chromatic Partitions, submitted.
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  4. Bressoud, D. M. (1981). Some identities for terminating q-series, Math. Proc. Cambridge Phil. Soc., 211–223.
  5. Lovejoy, J. (2004). Overpartitions, Trans. Amer. Math. Soc., 356, 1623–1635.
  6. Lovejoy, J. (2006). Overpartitions Pairs, Ann. Inst. Fourier (Grenoble), 56, 781–794.
  7. Lovejoy, J. (2007). Partitions and overpartitions with attached parts, Arch. Math., 88, 316–322.
  8. Pak, I. (2006). Partition Bijections, a Survey, Ramanujan Journal, 12, 5–75.

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Cite this paper

APA

Alegri, M. (2019). Bijective proofs involving chromatic overpartitions. Notes on Number Theory and Discrete Mathematics, 25(1), 128-136, doi: 10.7546/nntdm.2019.25.1.128-136.

Chicago

Alegri, Mateus. “Bijective Proofs Involving Chromatic Overpartitions.” Notes on Number Theory and Discrete Mathematics 25, no. 1 (2019): 128-136, doi: 10.7546/nntdm.2019.25.1.128-136.

MLA

Alegri, Mateus. “Bijective Proofs Involving Chromatic Overpartitions.” Notes on Number Theory and Discrete Mathematics 25.1 (2019): 128-136. Print, doi: 10.7546/nntdm.2019.25.1.128-136.

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