Alessandro Bagatini, Marília Luiza Matte and Adriana Wagner

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 25, 2019, Number 1, Pages 54—74

DOI: 10.7546/nntdm.2019.25.1.54-74

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## Details

### Authors and affiliations

Alessandro Bagatini

*IME, Universidade Federal do Rio Grande do Sul
Av. Bento Gonçalves, 9500 – 90509-900, Porto Alegre-RS, Brazil*

Present address: Instituto Federal Catarinense–IFC

88960-000, Sombrio-SC, Brazil

Marília Luiza Matte

*IME, Universidade Federal do Rio Grande do Sul
Av. Bento Gonçalves, 9500 – 90509-900, Porto Alegre-RS, Brazil*

Present address: Colégio Militar de Porto Alegre–CMPA

90040-130, Porto Alegre-RS, Brazil

Adriana Wagner

*IMECC–Universidade Estadual de Campinas
Rua Sérgio Buarque de Holanda, 651 – 13083-859, Campinas-SP, Brazil*

Present address: Campus de Aquidauana–UFMS

79200-000, Aquidauana-MS, Brazil

### Abstract

From two-line matrix interpretations of Mock Theta Functions *ρ*(*q*), *σ*(*q*) and *ν*(*q*) introduced in [5], we have obtained identities for the partitions generated by their respective general terms, whose proofs are done in a completely combinatorial way. We have also obtained relations between partitions into two colours generated by *ρ*(*q*) and *σ*(*q*), and also by *ν*(*q*).

### Keywords

- Mock Theta Function
- Integer partition
- Combinatorial interpretation
- Partition enumeration

### 2010 Mathematics Subject Classification

- 11P81
- 05A19

### References

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- Bagatini, A., Matte, M. L., & Wagner, A. (2017). Identities for partitions generated by the unsigned versions of some mock theta functions. Bulletin of the Brazilian Mathematical Society, New Series, Springer, 48 (3), 413–437.
- Brietzke, E. H. M., Santos, J. P. O., & da Silva, R. (2010). Bijective proofs using two-line matrix representations for partitions, The Ramanujan Journal, Springer, 23 (1–3), 265–295.
- Brietzke, E. H. M., Santos, J. P. O., & da Silva, R. (2013). Combinatorial interpretations as two-line array for the mock theta functions, Bulletin of the Brazilian Mathematical Society, New Series, Springer, 44 (2), 233–253.
- Santos, J. P. O., Mondek, P., & Ribeiro, A. C. (2011). New two-line arrays representing partitions, Annals of Combinatorics, Springer, 15 (2), 341–354.
- Wagner, A., Bagatini, A., & Matte, M. (2017). On new results about partitions into parts congruent to ±1 (mod 5), Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 5 (1), Article 0226, 7 pages, DOI: 10.5540/03.2017.005.01. 0226.

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## Cite this paper

APABagatini, A., Matte, M. L., & Wagner, A. (2019). Partitions generated by Mock Theta Functions *ρ*(*q*), *σ*(*q*) and *ν*(*q*) and relations with partitions into distinct parts. Notes on Number Theory and Discrete Mathematics, 25(1), 54-74, doi: 10.7546/nntdm.2019.25.1.54-74.

Bagatini, Alessandro, Marília Luiza Matte and Adriana Wagner. “Partitions Generated by Mock Theta Functions *ρ*(*q*), *σ*(*q*) and *ν*(*q*) and Relations with Partitions into Distinct Parts.” Notes on Number Theory and Discrete Mathematics 25, no. 1 (2019): 54-74, doi: 10.7546/nntdm.2019.25.1.54-74.

Bagatini, Alessandro, Marília Luiza Matte and Adriana Wagner. “Partitions Generated by Mock Theta Functions *ρ*(*q*), *σ*(*q*) and *ν*(*q*) and Relations with Partitions into Distinct Parts.” Notes on Number Theory and Discrete Mathematics 25.1 (2019): 54-74. Print, doi: 10.7546/nntdm.2019.25.1.54-74.