Arrays and integers partitions

Authors

DOI:

https://doi.org/10.14393/BEJOM-v3-n5-2022-63097

Keywords:

Integers partitions, Matrix representations, Identities

Abstract

In this work, we present a study on the new matrix representations of partitions introduced in 2011, a promising tool in the integer partitions theory. All representations discussed here consist of two-line arrays, but with distincts defining conditions. We bring examples of representations for partitions with or whitout restrictions, in particular the partitions of the first and second Rogers-Ramanujan identities. We seek to highlight some of the main uses of matrix representations in theory and the next steps that can be taken in future works on the subject. We end with results about matrix representations related to Schur's Identity.

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Author Biographies

Igor Vallis Christ, Federal University of São Carlos

Master's student in the Graduate Program in Mathematics at the Federal University of São Carlos. Graduate diploma in Mathematics by the Federal University of Espírito Santo. He was a fellow at the Institutional Scholarship Program for Teaching Initiation (PIBID) and a fellow at CNPq and UFES in two scientific initiation projects on integer partitions. He also acted as tutor of the linear algebra course.

Victor Martins, State University of Campinas

PhD in Mathematics by the State University of Campinas (2017), with a sandwich period at the Universitat zu Koln in 2015. Master in Mathematics by the Federal University of Viçosa (2013). Graduate diploma in Mathematics by the Federal University of Viçosa (2011). He is currently an Adjunct Professor at the Federal University of Espírito Santo (UFES). Has experience in Mathematics with an emphasis
on Algebra. Interested in the following topics: error correcting codes; representations of Lie algebras.

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Published

2022-06-02

How to Cite

CHRIST, I. V.; MARTINS, V. Arrays and integers partitions. BRAZILIAN ELECTRONIC JOURNAL OF MATHEMATICS, Uberlândia, v. 3, n. 5, 2022. DOI: 10.14393/BEJOM-v3-n5-2022-63097. Disponível em: https://seer.ufu.br/index.php/BEJOM/article/view/63097. Acesso em: 19 nov. 2024.

Issue

Vol. 3 No. 5 (2022): Brazilian Electronic Journal of Mathematics

Section

Articles - Pure Mathematics

License

Copyright (c) 2022 BRAZILIAN ELECTRONIC JOURNAL OF MATHEMATICS

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